Collective dynamics in entangled worm and robot blobs

Inertia and activity: spiral transitions in semi-flexible, self-avoiding polymers

We consider a two-dimensional, tangentially active, semi-flexible, self-avoiding polymer to find a dynamical re-entrant transition between motile open chains and spinning achiral spirals with increasing activity. Utilizing probability distributions of the turning number, we ascertain the comparative stability of the spiral structure and present a detailed phase diagram within the activity inertia plane. The onset of spiral formation at low activity levels is governed by a torque balance and is independent of inertia. At higher activities, however, inertial effects lead to spiral destabilization, an effect absent in the overdamped limit. We further delineate alterations in size and shape by analyzing the end-to-end distance distribution and the radius of gyration tensor. The Kullback-Leibler divergence from equilibrium distributions exhibits a non-monotonic relationship with activity, reaching a peak at the most compact spirals characterized by the most persistent spinning. As inertia increases, this divergence from equilibrium diminishes.

Leeches Predate on Fast-Escaping and Entangling Blackworms by Spiral Entombment

We investigate how the Helobdella spp. freshwater leeches capture and consume Lumbriculus variegatus blackworms despite the blackworm's ultrafast helical swimming escape reflex and ability to form large tangled 'blobs'. We describe our discovery of a unique spiral 'entombment' strategy used by these leeches to overcome the blackworms' active and collective defenses. Unlike their approach to less reactive and solitary prey like mollusks, where leeches simply attach and suck, Helobdella leeches employ this spiral entombment strategy specifically adapted for blackworms. Our findings highlight the complex interactions between predator and prey in freshwater ecosystems, providing insights into ecological adaptability and predator-prey dynamics.

Non-equilibrium structural and dynamic behaviors of active polymers in complex and crowded environments

Active matter systems, which convert internal chemical energy or energy from the environment into directed motion, are ubiquitous in nature and exhibit a range of emerging non-equilibrium behaviors. However, most of the current works on active matter have been devoted to particles, and the study of active polymers has only recently come into the spotlight due to their prevalence within living organisms. The intricate interplay between activity and conformational degrees of freedom gives rise to novel structural and dynamical behaviors of active polymers. Research in active polymers remarkably broadens diverse concepts of polymer physics, such as molecular architecture, dynamics, scaling and so on, which is of significant importance for the development of new polymer materials with unique performance. Furthermore, active polymers are often found in strongly interacting and crowded systems and in complex environments, so that the understanding of this behavior is essential for future developments of novel polymer-based biomaterials. This review thereby focuses on the study of active polymers in complex and crowded environments, and aims to provide insights into the fundamental physics underlying the adaptive and collective behaviors far from equilibrium, as well as the open challenges that the field is currently facing.

Self-Organized States from Solutions of Active Ring Polymers in Bulk and under Confinement

In the present work, we study, by means of numerical simulations, the structural and dynamical behavior of a suspension of active ring polymers in bulk and under lateral confinement. At high activity, when changing the distance between the confining planes and the polymers' density, we identify the emergence of a self-organized dynamical state, characterized by the coexistence of slowly diffusing clusters of rotating disks and faster rings moving in between them. We further assess that self-organization is robust in a range of polymer sizes, and we identify a critical value of the activity, necessary to trigger cluster formation. This system has distinctive features resembling at the same time polymers, liquid crystals, and active systems, where the interplay between activity, topology, and confinement leads to a spontaneous segregation in an initially one-component solution.

Conformation and dynamics of partially active linear polymers

We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along the chain determines the conformational and dynamical properties of the system. Notably, one can modulate the diffusion coefficient of the polymer from active-like to passive-like just by changing the position of the active block. Further, we show that a slight modification of the self-propulsion rule may give rise to an enhancement of diffusion under certain conditions, despite a decrease of the overall polymer activity. Our findings may help in the modelisation of active biophysical systems, such as filamentous bacteria or worms.

Material assembly from collective action of shape-changing polymers

Some animals form transient, responsive and solid-like ensembles through dynamic structural interactions. These ensembles demonstrate emergent responses such as spontaneous self-assembly, which are difficult to achieve in synthetic soft matter. Here we use shape-morphing units comprising responsive polymers to create solids that self-assemble, modulate their volume and disassemble on demand. The ensemble is composed of a responsive hydrogel, liquid crystal elastomer or semicrystalline polymer ribbons that reversibly bend or twist. The dispersions of these ribbons mechanically interlock, inducing reversible aggregation. The aggregated liquid crystal elastomer ribbons have a 12-fold increase in the yield stress compared with cooled dispersion and contract by 34% on heating. Ribbon type, concentration and shape dictate the aggregation and govern the global mechanical properties of the solid that forms. Coating liquid crystal elastomer ribbons with a liquid metal begets photoresponsive and electrically conductive aggregates, whereas seeding cells on hydrogel ribbons enables self-assembling three-dimensional scaffolds, providing a versatile platform for the design of dynamic materials.

Long-range ordering of velocity-aligned active polymers

In this work, we study the effect of covalent bonding on the behavior of non-equilibrium systems with the active force acting on particles along their velocity. Self-ordering of single particles does not occur in this model. However, starting from some critical polymerization degree, the ordered state is observed. It is homogeneous and exhibits no phase separation. In the ordered state, the chains prefer a near-two-dimensional configuration and all move in one direction. Importantly, the self-ordering is obtained only at intermediate active force magnitudes. At high magnitudes, the transition from the disordered to ordered state is suppressed by the swelling of the chains during the transition, as we show by the transition kinetics analysis. We demonstrate the bistable behavior of the system in a particular range of polymerization degrees, amplitudes of active force, densities, and thermostat temperatures. Overall, we show that covalent bonding greatly aids the self-ordering in this active particle model, in contrast to active Brownian particles.

Collecting-Gathering Biophysics of the Blackworm Lumbriculus variegatus

Many organisms exhibit collecting and gathering behaviors as a foraging and survival method. Benthic macroinvertebrates are classified as collector-gatherers due to their collection of particulate matter. Among these, the aquatic oligochaete Lumbriculus variegatus (California blackworms) demonstrates the ability to ingest both organic and inorganic materials, including microplastics. However, earlier studies have only qualitatively described their collecting behaviors for such materials. The mechanism by which blackworms consolidate discrete particles into a larger clump remains unexplored quantitatively. In this study, we analyze a group of blackworms in a large arena with an aqueous algae solution (organic particles) and find that their relative collecting efficiency is proportional to population size. We found that doubling the population size (N = 25-N = 50) results in a decrease in time to reach consolidation by more than half. Microscopic examination of individual blackworms reveals that both algae and microplastics physically adhere to the worm's body and form clumps due to external mucus secretions by the worms. Our observations also indicate that this clumping behavior reduces the worm's exploration of its environment, possibly due to thigmotaxis. To validate these observed biophysical mechanisms, we create an active polymer model of a worm moving in a field of particulate debris. We simulate its adhesive nature by implementing a short-range attraction between the worm and the nearest surrounding particles. Our findings indicate an increase in gathering efficiency when we add an attractive force between particles, simulating the worm's mucosal secretions. Our work provides a detailed understanding of the complex mechanisms underlying the collecting-gathering behavior in L. variegatus, informing the design of bioinspired synthetic collector systems, and advances our understanding of the ecological impacts of microplastics on benthic invertebrates.

Multichannel measurements of C. elegans largest Lyapunov exponents using optical diffraction

Dynamic diffraction (DOD) is a form of microscopy that allows the dynamic tracking of changing shapes in a 1D time series. DOD can capture the locomotion of a nematode while swimming freely in a 3D space, allowing the locomotion of the worm to more closely mimic natural behavior than in some other laboratory environments. More importantly, we are able to see markers of chaos as DOD covers dynamics on multiple length scales. This work introduces a multichannel method to measure the dynamic complexity of microscopic organisms. We show that parameters associated with chaos, such as the largest Lyapunov exponent (LLE), the mean frequency, mutual information (MI), and the embedding dimension, are independent of the specific point sampled in the diffraction pattern, thus demonstrating experimentally the consistency of our dynamic parameters sampled at various locations (channels) in the associated optical far-field pattern.

Worm blobs as entangled living polymers: from topological active matter to flexible soft robot collectives

Recently, the study of long, slender living worms has gained attention due to their unique ability to form highly entangled physical structures, exhibiting emergent behaviors. These organisms can assemble into an active three-dimensional soft entity referred to as the "blob", which exhibits both solid-like and liquid-like properties. This blob can respond to external stimuli such as light, to move or change shape. In this perspective article, we acknowledge the extensive and rich history of polymer physics, while illustrating how these living worms provide a fascinating experimental platform for investigating the physics of active, polymer-like entities. The combination of activity, long aspect ratio, and entanglement in these worms gives rise to a diverse range of emergent behaviors. By understanding the intricate dynamics of the worm blob, we could potentially stimulate further research into the behavior of entangled active polymers, and guide the advancement of synthetic topological active matter and bioinspired tangling soft robot collectives.

Elongating, entwining, and dragging: mechanism for adaptive locomotion of tubificine worm blobs in a confined environment

Worms often aggregate through physical connections and exhibit remarkable functions such as efficient migration, survival under environmental changes, and defense against predators. In particular, entangled blobs demonstrate versatile behaviors for their survival; they form spherical blobs and migrate collectively by flexibly changing their shape in response to the environment. In contrast to previous studies on the collective behavior of worm blobs that focused on locomotion in a flat environment, we investigated the mechanisms underlying their adaptive motion in confined environments, focusing on tubificine worm collectives. We first performed several behavioral experiments to observe the aggregation process, collective response to aversive stimuli, the motion of a few worms, and blob motion in confined spaces with and without pegs. We found the blob deformed and passed through a narrow passage using environmental heterogeneities. Based on these behavioral findings, we constructed a simple two-dimensional agent-based model wherein the flexible body of a worm was described as a cross-shaped agent that could deform, rotate, and translate. The simulations demonstrated that the behavioral findings were well-reproduced. Our findings aid in understanding how physical interactions contribute to generating adaptive collective behaviors in real-world environments as well as in designing novel swarm robotic systems consisting of soft agents.

Effects of inertia on conformation and dynamics of tangentially driven active filaments

Active filamentlike systems propelling along their backbone exist across scales ranging from motor-driven biofilaments to worms and robotic chains. In macroscopic active filaments such as a chain of robots, in contrast to their microscopic counterparts, inertial effects on their motion cannot be ignored. Nonetheless, the consequences of the interplay between inertia and flexibility on the shape and dynamics of active filaments remain unexplored. Here we examine inertial effects on a flexible tangentially driven active polymer model pertinent to the above examples and we determine the conditions under which inertia becomes important. Performing Langevin dynamics simulations of active polymers with underdamped and overdamped dynamics for a wide range of contour lengths and activities, we uncover striking inertial effects on conformation and dynamics for high levels of activities. Inertial collisions increase the persistence length of active polymers and remarkably alter their scaling behavior. In stark contrast to passive polymers, inertia leaves its fingerprint at long times by an enhanced diffusion of the center of mass. We rationalize inertia-induced enhanced dynamics by analytical calculations of center-of-mass velocity correlations, applicable to any active polymer model, which reveal significant contributions from active force fluctuations convoluted by inertial relaxation.

A simple mechanism for collective decision-making in the absence of payoff information

Animals are often faced with time-critical decisions without prior information about their actions' outcomes. In such scenarios, individuals budget their investment into the task to cut their losses in case of an adverse outcome. In animal groups, this may be challenging because group members can only access local information, and consensus can only be achieved through distributed interactions among individuals. Here, we combined experimental analyses with theoretical modeling to investigate how groups modulate their investment into tasks in uncertain conditions. Workers of the arboreal weaver ant Oecophylla smaragdina form three-dimensional chains using their own bodies to bridge vertical gaps between existing trails and new areas to explore. The cost of a chain increases with its length because ants participating in the structure are prevented from performing other tasks. The payoffs of chain formation, however, remain unknown to the ants until the chain is complete and they can explore the new area. We demonstrate that weaver ants cap their investment into chains, and do not form complete chains when the gap is taller than 90 mm. We show that individual ants budget the time they spend in chains depending on their distance to the ground, and propose a distance-based model of chain formation that explains the emergence of this tradeoff without the need to invoke complex cognition. Our study provides insights into the proximate mechanisms that lead individuals to engage (or not) in collective actions and furthers our knowledge of how decentralized groups make adaptive decisions in uncertain conditions.

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.

De novo evolution of macroscopic multicellularity

While early multicellular lineages necessarily started out as relatively simple groups of cells, little is known about how they became Darwinian entities capable of sustained multicellular evolution1-3. Here we investigate this with a multicellularity long-term evolution experiment, selecting for larger group size in the snowflake yeast (Saccharomyces cerevisiae) model system. Given the historical importance of oxygen limitation4, our ongoing experiment consists of three metabolic treatments5-anaerobic, obligately aerobic and mixotrophic yeast. After 600 rounds of selection, snowflake yeast in the anaerobic treatment group evolved to be macroscopic, becoming around 2 × 104 times larger (approximately mm scale) and about 104-fold more biophysically tough, while retaining a clonal multicellular life cycle. This occurred through biophysical adaptation-evolution of increasingly elongate cells that initially reduced the strain of cellular packing and then facilitated branch entanglements that enabled groups of cells to stay together even after many cellular bonds fracture. By contrast, snowflake yeast competing for low oxygen5 remained microscopic, evolving to be only around sixfold larger, underscoring the critical role of oxygen levels in the evolution of multicellular size. Together, this research provides unique insights into an ongoing evolutionary transition in individuality, showing how simple groups of cells overcome fundamental biophysical limitations through gradual, yet sustained, multicellular evolution.

Collecting-Gathering Biophysics of the Blackworm L. variegatus

Many organisms exhibit collecting and gathering behaviors as a foraging and survival method. Certain benthic macroinvertebrates are classified as collector-gatherers due to their collection of particulate matter as a food source, such as the aquatic oligochaete Lumbriculus variegatus (California blackworms). Blackworms demonstrate the ability to ingest organic and inorganic materials, including microplastics, but previous work has only qualitatively described their possible collecting behaviors for such materials. The mechanism through which blackworms consolidate discrete particles into a larger clumps remains unexplored quantitatively. By analyzing a group of blackworms in a large arena with an aqueous algae solution, we discover that their relative collecting efficiency is proportional to population size. Examining individual blackworms under a microscope reveals that both algae and microplastics physically adhere to the worm's body due to external mucus secretions, which cause the materials to clump around the worm. We observe that this clumping reduces the worm's exploration of its environment, potentially due to thigmotaxis. To validate the observed biophysical mechanisms, we create an active polymer model of a worm moving in a field of particulate debris with a short-range attractive force on its body to simulate its adhesive nature. We find that the attractive force increases gathering efficiency. This study offers insights into the mechanisms of collecting-gathering behavior, informing the design of robotic systems, as well as advancing our understanding the ecological impacts of microplastics on benthic invertebrates.

Ultrafast reversible self-assembly of living tangled matter

Tangled active filaments are ubiquitous in nature, from chromosomal DNA and cilia carpets to root networks and worm collectives. How activity and elasticity facilitate collective topological transformations in living tangled matter is not well understood. We studied California blackworms (Lumbriculus variegatus), which slowly form tangles in minutes but can untangle in milliseconds. Combining ultrasound imaging, theoretical analysis, and simulations, we developed and validated a mechanistic model that explains how the kinematics of individual active filaments determines their emergent collective topological dynamics. The model reveals that resonantly alternating helical waves enable both tangle formation and ultrafast untangling. By identifying generic dynamical principles of topological self-transformations, our results can provide guidance for designing classes of topologically tunable active materials.

Self-Oscillation and Synchronization Transitions in Elastoactive Structures

The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Among these, spontaneous self-oscillations of mechanical structures is perhaps the simplest and most widespread type of nonequilibrium phenomenon. Yet, we lack experimental model systems to investigate the various dynamical phenomena that may appear. Here, we introduce a centimeter-sized model system for one-dimensional elastoactive structures. We show that such structures exhibit flagellar motion when pinned at one end, self-snapping when pinned at two ends, and synchronization when coupled together with a sufficiently stiff link. We further demonstrate that these transitions can be described quantitatively by simple models of coupled pendula with follower forces. Beyond the canonical case considered here, we anticipate our work to open avenues for the understanding and design of the self-organization and response of active biological and synthetic solids, e.g., in higher dimensions and for more intricate geometries.

Ontogeny of collective behaviour

During their lifetime, superorganisms, like unitary organisms, undergo transformations that change the machinery of their collective behaviour. Here, we suggest that these transformations are largely understudied and propose that more systematic research into the ontogeny of collective behaviours is needed if we hope to better understand the link between proximate behavioural mechanisms and the development of collective adaptive functions. In particular, certain social insects engage in self-assemblage, forming dynamic and physically connected architectures with striking similarities to developing multicellular organisms, making them good model systems for ontogenetic studies of collective behaviour. However, exhaustive time series and three-dimensional data are required to thoroughly characterize the different life stages of the collective structures and the transitions between these stages. The well-established fields of embryology and developmental biology offer practical tools and theoretical frameworks that could speed up the acquisition of new knowledge about the formation, development, maturity and dissolution of social insect self-assemblages and, by extension, other superorganismal behaviours. We hope that this review will encourage an expansion of the ontogenetic perspective in the field of collective behaviour and, in particular, in self-assemblage research, which has far-reaching applications in robotics, computer science and regenerative medicine. This article is part of a discussion meeting issue 'Collective behaviour through time'.

Amorphous entangled active matter

The design of amorphous entangled systems, specifically from soft and active materials, has the potential to open exciting new classes of active, shape-shifting, and task-capable 'smart' materials. However, the global emergent mechanics that arise from the local interactions of individual particles are not well understood. In this study, we examine the emergent properties of amorphous entangled systems in an in silico collection of u-shaped particles ("smarticles") and in living entangled aggregate of worm blobs (L. variegatus). In simulations, we examine how material properties change for a collective composed of smarticles as they undergo different forcing protocols. We compare three methods of controlling entanglement in the collective: external oscillations of the ensemble, sudden shape-changes of all individuals, and sustained internal oscillations of all individuals. We find that large-amplitude changes of the particle's shape using the shape-change procedure produce the largest average number of entanglements, with respect to the aspect ratio (l/w), thus improving the tensile strength of the collective. We demonstrate applications of these simulations by showing how the individual worm activity in a blob can be controlled through the ambient dissolved oxygen in water, leading to complex emergent properties of the living entangled collective, such as solid-like entanglement and tumbling. Our work reveals principles by which future shape-modulating, potentially soft robotic systems may dynamically alter their material properties, advancing our understanding of living entangled materials, while inspiring new classes of synthetic emergent super-materials.

Morphological computation and decentralized learning in a swarm of sterically interacting robots

Whereas naturally occurring swarms thrive when crowded, physical interactions in robotic swarms are either avoided or carefully controlled, thus limiting their operational density. Here, we present a mechanical design rule that allows robots to act in a collision-dominated environment. We introduce Morphobots, a robotic swarm platform developed to implement embodied computation through a morpho-functional design. By engineering a three-dimensional printed exoskeleton, we encode a reorientation response to an external body force (such as gravity) or a surface force (such as a collision). We show that the force orientation response is generic and can augment existing swarm robotic platforms (e.g., Kilobots) as well as custom robots even 10 times larger. At the individual level, the exoskeleton improves motility and stability and also allows encoding of two contrasting dynamical behaviors in response to an external force or a collision (including collision with a wall or a movable obstacle and on a dynamically tilting plane). This force orientation response adds a mechanical layer to the robot's sense-act cycle at the swarm level, leveraging steric interactions for collective phototaxis when crowded. Enabling collisions also promotes information flow, facilitating online distributed learning. Each robot runs an embedded algorithm that ultimately optimizes collective performance. We identify an effective parameter that controls the force orientation response and explore its implications in swarms that transition from dilute to crowded. Experimenting with physical swarms (of up to 64 robots) and simulated swarms (of up to 8192 agents) shows that the effect of morphological computation increases with growing swarm size.

A mesoscale agent based modeling framework for flow-mediated infection transmission in indoor occupied spaces

The ongoing Covid-19 pandemic, and its associated public health and socioeconomic burden, has reaffirmed the necessity for a comprehensive understanding of flow-mediated infection transmission in occupied indoor spaces. This is an inherently multiscale problem, and suitable investigation approaches that can enable evidence-based decision-making for infection control strategies, interventions, and policies; will need to account for flow physics, and occupant behavior. Here, we present a mesoscale infection transmission model for human occupied indoor spaces, by integrating an agent-based human interaction model with a flow physics model for respiratory droplet dynamics and transport. We outline the mathematical and algorithmic details of the modeling framework, and demonstrate its validity using two simple simulation scenarios that verify each of the major sub-models. We then present a detailed case-study of infection transmission in a model indoor space with 60 human occupants; using a systematic set of simulations representing various flow scenarios. Data from the simulations illustrate the utility and efficacy of the devised mesoscale model in resolving flow-mediated infection transmission; and elucidate key trends in infection transmission dynamics amongst the human occupants.

Active entanglement enables stochastic, topological grasping

Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception and motion planning. Here, we circumvent the need for feedback or precise planning by using an array of fluidically actuated slender hollow elastomeric filaments to actively entangle with objects that vary in geometric and topological complexity. The resulting stochastic interactions enable a unique soft and conformable grasping strategy across a range of target objects that vary in size, weight, and shape. We experimentally evaluate the grasping performance of our strategy and use a computational framework for the collective mechanics of flexible filaments in contact with complex objects to explain our findings. Overall, our study highlights how active collective entanglement of a filament array via an uncontrolled, spatially distributed scheme provides options for soft, adaptable grasping.

Drug-loaded IRONSperm clusters: modeling, wireless actuation, and ultrasound imaging

Individual biohybrid microrobots have the potential to perform biomedical in vivo tasks such as remote-controlled drug and cell delivery and minimally invasive surgery. This work demonstrates the formation of biohybrid sperm-templated clusters under the influence of an external magnetic field and essential functionalities for wireless actuation and drug delivery. Ferromagnetic nanoparticles are electrostatically assembled around dead sperm cells, and the resulting nanoparticle-coated cells are magnetically assembled into threedimensional biohybrid clusters. The aim of this clustering is threefold: First, to enable rolling locomotion on a nearby solid boundary using a rotating magnetic field; second, to allow for noninvasive localization; third, to load the cells inside the cluster with drugs for targeted delivery. A magneto-hydrodynamic model captures the rotational response of the clusters in a viscous fluid, and predicts an upper bound for their step-out frequency, which is independent of their volume or aspect ratio. Below the step-out frequency, the rolling velocity of the clusters increases nonlinearly with their perimeter and actuation frequency. During rolling locomotion, the clusters are localized using ultrasound at a relatively large distance, which makes these biohybrid clusters promising for deep-tissue applications. Finally, we show that the estimated drug load scales with the number of cells in the cluster and can be retained for more than 10 hours. The aggregation of microrobots enables them to collectively roll in a predictable way in response to an external rotating magnetic field, and enhances ultrasound detectability and drug loading capacity compared to the individual microrobots. The favorable features of biohybrid microrobot clusters place emphasis on the importance of the investigation and development of collective microrobots and their potential for in vivo applications.

From the origin of life to pandemics: emergent phenomena in complex systems

When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This non-trivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems-from physical to biological and social-and is often related to collective behaviour. It is ubiquitous, from non-living entities such as oscillators that under specific conditions synchronize, to living ones, such as birds flocking or fish schooling. Despite the ample phenomenological evidence of the existence of systems' emergent properties, central theoretical questions to the study of emergence remain unanswered, such as the lack of a widely accepted, rigorous definition of the phenomenon or the identification of the essential physical conditions that favour emergence. We offer here a general overview of the phenomenon of emergence and sketch current and future challenges on the topic. Our short review also serves as an introduction to the theme issue Emergent phenomena in complex physical and socio-technical systems: from cells to societies, where we provide a synthesis of the contents tackled in the issue and outline how they relate to these challenges, spanning from current advances in our understanding on the origin of life to the large-scale propagation of infectious diseases. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Oxygenation-Controlled Collective Dynamics in Aquatic Worm Blobs

Many organisms utilize group aggregation as a method for survival. The freshwater oligochaete, Lumbriculus variegatus (California blackworms) form tightly entangled structures, or worm "blobs", that have adapted to survive in extremely low levels of dissolved oxygen (DO). Individual blackworms adapt to hypoxic environments through respiration via their mucous body wall and posterior ciliated hindgut, which they wave above them. However, the change in collective behavior at different levels of DO is not known. Using a closed-loop respirometer with flow, we discover that the relative tail reaching activity flux in low DO is ∼75x higher than in the high DO condition. Additionally, when flow rate is increased to suspend the worm blobs upward, we find that the average exposed surface area of a blob in low DO is ∼1.4x higher than in high DO. Furthermore, we observe emergent properties that arise when a worm blob is exposed to extreme DO levels. We demonstrate that internal mechanical stress is generated when worm blobs are exposed to high DO levels, allowing them to be physically lifted off from the bottom of a conical container using a serrated endpiece. Our results demonstrate how both collective behavior and the emergent generation of internal mechanical stress in worm blobs change to accommodate differing levels of oxygen. From an engineering perspective, this could be used to model and simulate swarm robots, self-assembly structures, or soft material entanglements.

Chromatographic separation of active polymer-like worm mixtures by contour length and activity

The convective transport rate of polymers through confined geometries depends on their size, allowing for size-based separation of polymer mixtures (chromatography). Here, we investigate whether mixtures of active polymers can be separated in a similar manner based on their activity. We use thin, living Tubifex tubifex worms as a model system for active polymers and study the transport of these worms by an imposed flow through a channel filled with a hexagonal pillar array. The transport rate through the channel depends strongly on the degree of activity, an effect that we assign to the different distribution of conformations sampled by the worms depending on their activity. Our results demonstrate a unique way to sort mixtures of active polymers based on their activity and provide a versatile and convenient experimental system to investigate the hydrodynamics of active polymers.

Lateral contact yields longitudinal cohesion in active undulatory systems

Many animals and robots move using undulatory motion of their bodies. When the bodies are in close proximity undulatory motion can lead to novel collective behavior such as gait synchronization, spatial reconfiguration, and clustering. Here we study the role of contact interactions between model undulatory swimmers: three-link robots in experiment and multilink swimmers in simulation. The undulatory gait of each swimmer is generated through a time-dependent sinusoidal-like waveform which has a fixed phase offset, ϕ. By varying the phase relationship between neighboring swimmers we seek to study how contact forces and planar configurations are governed by the phase difference between neighboring swimmers. We find that undulatory actuation in close proximity drives neighboring swimmers into planar equilibrium configurations that depend on the actuation phase difference. We propose a model for stable planar configurations of nearest-neighbor undulatory swimmers which we call the gait compatibility condition, which is the set of planar and phase configurations in which no collisions occur. Robotic experiments with two, three, and four swimmers exhibit good agreement with the compatibility model. To study the contact forces and the time-averaged equilibrium between undulatory systems we perform simulations. To probe the interaction potential between undulatory swimmers we apply a small force to each swimmer longitudinally to separate them from the compatible configuration and we measure their steady-state displacement. These studies reveal that undulatory swimmers in close proximity exhibit attractive longitudinal interaction forces that drive the swimmers from incompatible to compatible configurations. This system of undulatory swimmers provides new insight into active-matter systems which move through body undulation. In addition to the importance of velocity and orientation coherence in active-matter swarms, we demonstrate that undulatory phase coherence is also important for generating stable, cohesive group configurations.

Heterogeneity-induced lane and band formation in self-driven particle systems

The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and nonuniform patterns. In this article, we investigate the effects of different types of heterogeneity in a two-species self-driven particle system. We show that heterogeneity can generically initiate segregation in the motion and identify two heterogeneity mechanisms. Longitudinal lanes parallel to the direction of motion emerge when the heterogeneity statically lies in the agent characteristics (quenched disorder). While transverse bands orthogonal to the motion direction arise from dynamic heterogeneity in the interactions (annealed disorder). In both cases, non-linear transitions occur as the heterogeneity increases, from disorder to ordered states with lane or band patterns. These generic features are observed for a first and a second order motion model and different characteristic parameters related to particle speed and size. Simulation results show that the collective dynamics occur in relatively short time intervals, persist stationary, and are partly robust against random perturbations.

Synchronized oscillations in swarms of nematode Turbatrix aceti

There is a recent surge of interest in the behavior of active particles that can at the same time align their direction of movement and synchronize their oscillations, known as swarmalators. While theoretical and numerical models of such systems are now abundant, no real-life examples have been shown to date. We present an experimental investigation of the collective motion of the nematode Turbatrix aceti that self-propel by body undulation. We discover that these nematodes can synchronize their body oscillations, forming striking traveling metachronal waves, which produces strong fluid flows. We uncover that the location and strength of this collective state can be controlled through the shape of the confining structure; in our case the contact angle of a droplet. This opens a way for producing controlled work such as on-demand flows or displacement of objects. We illustrate this by showing that the force generated by this state is sufficient to change the physics of evaporation of fluid droplets, by counteracting the surface-tension force, which allow us to estimate its strength. The relatively large size and ease of culture make Turbatrix aceti a promising model organism for experimental investigation of swarming and oscillating active matter capable of producing controllable work.

Computational exploration of treadmilling and protrusion growth observed in fire ant rafts

Collective living systems regularly achieve cooperative emergent functions that individual organisms could not accomplish alone. The rafts of fire ants (Solenopsis invicta) are often studied in this context for their ability to create aggregated structures comprised entirely of their own bodies, including tether-like protrusions that facilitate exploration of and escape from flooded environments. While similar protrusions are observed in cytoskeletons and cellular aggregates, they are generally dependent on morphogens or external gradients leaving the isolated role of local interactions poorly understood. Here we demonstrate through an ant-inspired, agent-based numerical model how protrusions in ant rafts may emerge spontaneously due to local interactions. The model is comprised of a condensed structural network of agents that represents the monolayer of interconnected worker ants, which floats on the water and gives ant rafts their form. Experimentally, this layer perpetually contracts, which we capture through the pairwise contraction of all neighboring structural agents at a strain rate of [Formula: see text]. On top of the structural layer, we model a dispersed, on-lattice layer of motile agents that represents free ants, which walk on top of the floating network. Experimentally, these self-propelled free ants walk with some mean persistence length and speed that we capture through an ant-inspired phenomenological model. Local interactions occur between neighboring free ants within some radius of detection, R, and the persistence length of freely active agents is tuned through a noise parameter, η as introduced by the Vicsek model. Both R and η where fixed to match the experimental trajectories of free ants. Treadmilling of the raft occurs as agents transition between the structural and free layers in accordance with experimental observations. Ultimately, we demonstrate how phases of exploratory protrusion growth may be induced by increased ant activity as characterized by a dimensionless parameter, [Formula: see text]. These results provide an example in which functional morphogenesis of a living system may emerge purely from local interactions at the constituent length scale, thereby providing a source of inspiration for the development of decentralized, autonomous active matter and swarm robotics.

Nematodes Follow a Leader

Aggregated movement and population structure are known in entomopathogenic nematodes, which are obligate insect parasites. Aggregation behavior in the absence of external stimuli suggests communication among individuals, often in the form of trail-following, which has not been shown by nematodes of any kind. Interactions among individuals are an essential basis of following behaviors and can have significant fitness consequences. We explored intraspecific and interspecific interactions among three Steinernema species (S. glaseri, S. carpocapsae, and S. feltiae) in terms of trail following, and fitness outcomes of following heterospecific individuals. We found that the following behavior is context dependent. Following behavior among conspecifics was significantly increased when the lead nematode had prior contact with host cuticle. However, we did not find a clear association between the following response to heterospecific IJs and their reproductive success in a co-infected host.