Out-of-equilibrium interactions and collective locomotion of colloidal spheres with squirming of nematoelastic multipoles

Many living and artificial systems show similar emergent behavior and collective motions on different scales, starting from swarms of bacteria to synthetic active particles, herds of mammals, and crowds of people. What all these systems often have in common is that new collective properties like flocking emerge from interactions between individual self-propelled or driven units. Such systems are naturally out-of-equilibrium and propel at the expense of consumed energy. Mimicking nature by making self-propelled or externally driven particles and studying their individual and collective motility may allow for deeper understanding of physical underpinnings behind collective motion of large groups of interacting objects or beings. Here, using a soft matter system of colloids immersed into a liquid crystal, we show that resulting so-called nematoelastic multipoles can be set into a bidirectional locomotion by external oscillating electric fields. Out-of-equilibrium elastic interactions between such colloidal objects lead to collective flock-like behaviors emerging from time-varying elasticity-mediated interactions between externally driven propelling particles. Repulsive elastic interactions in the equilibrium state can be turned into attractive interactions in the out-of-equilibrium state under applied external electric fields. We probe this behavior at different number densities of colloidal particles and show that particles in dense dispersions collectively select the same direction of a coherent motion due to elastic interactions between near neighbors. In our experimentally implemented design, their motion is highly ordered and without clustering or jamming often present in other colloidal transport systems, which is promising for technological and fundamental-science applications, like nano-cargo transport, out-of-equilibrium assembly, and microrobotics.

Magnetic Control of Nonmagnetic Living Organisms

Living organisms inspire the design of microrobots, but their functionality is unmatched. Next-generation microrobots aim to leverage the sensing and communication abilities of organisms through magnetic hybridization, attaching magnetic particles to them for external control. However, the protocols used for magnetic hybridization are morphology specific and are not generalizable. We propose an alternative approach that leverages the principles of negative magnetostatics and magnetophoresis to control nonmagnetic organisms with external magnetic fields. To do this, we disperse model organisms in dispersions of Fe3O4 nanoparticles and expose them to either uniform or gradient magnetic fields. In uniform magnetic fields, living organisms align with the field due to external torque, while gradient magnetic fields generate a negative magnetophoretic force, pushing objects away from external magnets. The magnetic fields enable controlling the position and orientation of Caenorhabditis elegans larvae and flagellated bacteria through directional interactions and magnitude. This control is diminished in live spermatozoa and adult C. elegans due to stronger internal biological activity, i.e., force/torque. Our study presents a method for spatiotemporal organization of living organisms without requiring magnetic hybridization, opening the way for the development of controllable living microbiorobots.

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

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

Activity-driven chromatin organization during interphase: compaction, segregation, and entanglement suppression

In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process called active loop extrusion. Chromosome conformation capture and imaging experiments have suggested that chromatin adopts a compact structure with limited interpenetration between chromosomes and between chromosomal sections. We developed a theory demonstrating that active loop extrusion causes the apparent fractal dimension of chromatin to cross over between two and four at contour lengths on the order of 30 kilo-base pairs (kbp). The anomalously high fractal dimension D = 4 is due to the inability of extruded loops to fully relax during active extrusion. Compaction on longer contour length scales extends within topologically associated domains (TADs), facilitating gene regulation by distal elements. Extrusion-induced compaction segregates TADs such that overlaps between TADs are reduced to less than 35% and increases the entanglement strand of chromatin by up to a factor of 50 to several Mega-base pairs. Furthermore, active loop extrusion couples cohesin motion to chromatin conformations formed by previously extruding cohesins and causes the mean square displacement of chromatin loci during lag times ( Δ t ) longer than tens of minutes to be proportional to Δ t 1 / 3 . We validate our results with hybrid molecular dynamics - Monte Carlo simulations and show that our theory is consistent with experimental data. This work provides a theoretical basis for the compact organization of interphase chromatin, explaining the physical reason for TAD segregation and suppression of chromatin entanglements which contribute to efficient gene regulation.

Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors

Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.

Induction for Self-Propelled Motion of Artificial Objects with/without Shape Anisotropy

Motion is an essential feature of living systems. Microorganisms autonomously change their nature in response to slight changes in the surrounding environment induced by external stimuli and exhibit unique motion modes. Various self-propelled objects have been constructed to understand these behaviors. Towards achievement of such purpose, the precise settings of experimental conditions including fabrication of objects with a shape anisotropy have been made attempts in the field of active matter and supramolecular chemistry. This review describes the recent progress in inducing the self-propelled motion of artificial objects. If life-like dynamic behavior such as self-propelled motion can be designed and experimentally induced from molecular properties, it will be easier to control functions expressed as outputs. This will lead to not only a better understanding of the complex functions in living systems, but also the fabrication of exotic materials with life-like properties.

Acoustically Powered Nano- and Microswimmers: From Individual to Collective Behavior

Micro- and nanoscopic particles that swim autonomously and self-assemble under the influence of chemical fuels and external fields show promise for realizing systems capable of carrying out large-scale, predetermined tasks. Different behaviors can be realized by tuning swimmer interactions at the individual level in a manner analogous to the emergent collective behavior of bacteria and mammalian cells. However, the limited toolbox of weak forces with which to drive these systems has made it difficult to achieve useful collective functions. Here, we review recent research on driving swimming and particle self-organization using acoustic fields, which offers capabilities complementary to those of the other methods used to power microswimmers. With either chemical or acoustic propulsion (or a combination of the two), understanding individual swimming mechanisms and the forces that arise between individual particles is a prerequisite to harnessing their interactions to realize collective phenomena and macroscopic functionality. We discuss here the ingredients necessary to drive the motion of microscopic particles using ultrasound, the theory that describes that behavior, and the gaps in our understanding. We then cover the combination of acoustically powered systems with other cross-compatible driving forces and the use of ultrasound in generating collective behavior. Finally, we highlight the demonstrated applications of acoustically powered microswimmers, and we offer a perspective on the state of the field, open questions, and opportunities. We hope that this review will serve as a guide to students beginning their work in this area and motivate others to consider research in microswimmers and acoustic fields.

Universal Poisson statistics of a passive tracer diffusing in dilute active suspensions

The statistics of a passive tracer immersed in a suspension of active particles (swimmers) is derived from first principles by considering a perturbative expansion of the tracer interaction with the microscopic swimmer field. To first order in the swimmer density, the tracer statistics is shown to be exactly represented by a spatial Poisson process combined with independent tracer-swimmer scattering events, rigorously reducing the multiparticle dynamics to two-body interactions. The Poisson representation is valid in any dimension, for arbitrary interaction forces and for a large class of swimmer dynamics. The framework not only allows for the systematic calculation of the tracer statistics in various dynamical regimes but highlights in particular surprising universal features that are independent of the swimmer dynamics such as a time-independent velocity distribution.

Spontaneous Chiral Symmetry Breaking and Lane Formation in Ferromagnetic Ferrofluids

Ferromagnetic ferrofluids are synthetic materials consisting of magnetic nanoplatelets dispersed in an isotropic fluid. Their main characteristics are the formation of stable magnetic domains and the presence of macroscopic magnetization even in the absence of a magnetic field. Here, the authors report on the experimental observation of spontaneous stripe formation in a ferromagnetic ferrofluid in the presence of an oscillating external magnetic field. The striped structure is identified as elongated magnetic domains, which exhibit reorientation upon reversal of the magnetic field. The stripes are oriented perpendicular to the magnetic field and are separated by alternating flow lanes. The velocity profile is measured using a space-time correlation technique that follows the motion of the thermally excited fluctuations in the sample. The highest velocities are found in the depleted regions between individual domains and reach values up to several µm s-1 . The fluid in adjacent lanes moves in the opposite directions despite the applied magnetic field being uniform. The formation of bidirectional flow lanes can be explained by alternating rotation of magnetic nanoparticles in neighboring stripes, which indicates spontaneous breaking of the chiral symmetry in the sample.

Platinum-DNA Origami Hybrid Structures in Concentrated Hydrogen Peroxide

The DNA origami technique allows fast and large-scale production of DNA nanostructures that stand out with an accurate addressability of their anchor points. This enables the precise organization of guest molecules on the surfaces and results in diverse functionalities. However, the compatibility of DNA origami structures with catalytically active matter, a promising pathway to realize autonomous DNA machines, has so far been tested only in the context of bio-enzymatic activity, but not in chemically harsh reaction conditions. The latter are often required for catalytic processes involving high-energy fuels. Here, we provide proof-of-concept data showing that DNA origami structures are stable in 5 % hydrogen peroxide solutions over the course of at least three days. We report a protocol to couple these to platinum nanoparticles and show catalytic activity of the hybrid structures. We suggest that the presented hybrid structures are suitable to realize catalytic nanomachines combined with precisely engineered DNA nanostructures.

Symmetrical Catalytic Colloids Display Janus-Like Active Brownian Particle Motion

Catalytic Janus colloids, with one hemi-sphere covered by a hydrogen peroxide reduction catalyst such as platinum, represent one of the most experimentally explored examples of self-motile active colloid systems. This paper comparatively investigates the motile behavior of symmetrical catalytic colloids produced by a solution-based metal salt reduction process. Despite the significant differences in the distribution of catalytic activity, this study finds that the motion produced by symmetrical colloids is equivalent to that previously reported for Janus colloids. It also shows that introducing a Janus structure to the symmetrical colloids via masking does not significantly modify their motion. These findings could indicate that very subtle variations in surface reactivity can be sufficient to produce Janus-like active Brownian particle-type motion, or that a symmetry-breaking phenomena is present. The study will consequently motivate fresh theoretical attention and also demonstrate a straightforward route to access large quantities of motile active colloids, which are expected to show subtly different phenomenology compared to those with Janus structures.

How it feels in a cell

Life emerges from thousands of biochemical processes occurring within a shared intracellular environment. We have gained deep insights from in vitro reconstitution of isolated biochemical reactions. However, the reaction medium in test tubes is typically simple and diluted. The cell interior is far more complex: macromolecules occupy more than a third of the space, and energy-consuming processes agitate the cell interior. Here, we review how this crowded, active environment impacts the motion and assembly of macromolecules, with an emphasis on mesoscale particles (10-1000 nm diameter). We describe methods to probe and analyze the biophysical properties of cells and highlight how changes in these properties can impact physiology and signaling, and potentially contribute to aging, and diseases, including cancer and neurodegeneration.

Measuring response functions of active materials from data

From flocks of birds to biomolecular assemblies, systems in which many individual components independently consume energy to perform mechanical work exhibit a wide array of striking behaviors. Methods to quantify the dynamics of these so-called active systems generally aim to extract important length or time scales from experimental fields. Because such methods focus on extracting scalar values, they do not wring maximal information from experimental data. We introduce a method to overcome these limitations. We extend the framework of correlation functions by taking into account the internal headings of displacement fields. The functions we construct represent the material response to specific types of active perturbation within the system. Utilizing these response functions we query the material response of disparate active systems composed of actin filaments and myosin motors, from model fluids to living cells. We show we can extract critical length scales from the turbulent flows of an active nematic, anticipate contractility in an active gel, distinguish viscous from viscoelastic dissipation, and even differentiate modes of contractility in living cells. These examples underscore the vast utility of this method which measures response functions from experimental observations of complex active systems.

Pair Interaction between Two Catalytically Active Colloids

Due to the intrinsically complex non-equilibrium behavior of the constituents of active matter systems, a comprehensive understanding of their collective properties is a challenge that requires systematic bottom-up characterization of the individual components and their interactions. For self-propelled particles, intrinsic complexity stems from the fact that the polar nature of the colloids necessitates that the interactions depend on positions and orientations of the particles, leading to a 2d - 1 dimensional configuration space for each particle, in d dimensions. Moreover, the interactions between such non-equilibrium colloids are generically non-reciprocal, which makes the characterization even more complex. Therefore, derivation of generic rules that enable us to predict the outcomes of individual encounters as well as the ensuing collective behavior will be an important step forward. While significant advances have been made on the theoretical front, such systematic experimental characterizations using simple artificial systems with measurable parameters are scarce. Here, two different contrasting types of colloidal microswimmers are studied, which move in opposite directions and show distinctly different interactions. To facilitate the extraction of parameters, an experimental platform is introduced in which these parameters are confined on a 1D track. Furthermore, a theoretical model for interparticle interactions near a substrate is developed, including both phoretic and hydrodynamic effects, which reproduces their behavior. For subsequent validation, the degrees of freedom are increased to 2D motion and resulting trajectories are predicted, finding remarkable agreement. These results may prove useful in characterizing the overall alignment behavior of interacting self-propelling active swimmer and may find direct applications in guiding the design of active-matter systems involving phoretic and hydrodynamic interactions.

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.

Active-matter isomorphs in the size-polydisperse Ornstein-Uhlenbeck Lennard-Jones model

This paper studies size-polydisperse Lennard-Jones systems described by active Ornstein-Uhlenbeck particle (AOUP) dynamics. The focus is on the existence of isomorphs (curves of invariant structure and dynamics) in the model's three-dimensional phase diagram. Isomorphs are traced out from a single steady-state configuration by means of the configurational-temperature method. Good isomorph invariance of the reduced-unit radial distribution function and the mean-square displacement as a function of time is demonstrated for three uniform-distribution polydispersities,12%, 23%, and 29%. Comparing to active-matter isomorphs generated by the analytical direct-isomorph-check method, the latter have poorer invariance of the structure, but better invariance of the dynamics. We conclude that both methods can be used to quickly get an overview of the phase diagram of polydisperse AOUP models involving a potential-energy function obeying the hidden-scale-invariance property required for isomorph theory to apply.

Kinesin and myosin motors compete to drive rich multiphase dynamics in programmable cytoskeletal composites

The cellular cytoskeleton relies on diverse populations of motors, filaments, and binding proteins acting in concert to enable nonequilibrium processes ranging from mitosis to chemotaxis. The cytoskeleton's versatile reconfigurability, programmed by interactions between its constituents, makes it a foundational active matter platform. However, current active matter endeavors are limited largely to single force-generating components acting on a single substrate-far from the composite cytoskeleton in cells. Here, we engineer actin-microtubule (MT) composites, driven by kinesin and myosin motors and tuned by crosslinkers, to ballistically restructure and flow with speeds that span three orders of magnitude depending on the composite formulation and time relative to the onset of motor activity. Differential dynamic microscopy analyses reveal that kinesin and myosin compete to delay the onset of acceleration and suppress discrete restructuring events, while passive crosslinking of either actin or MTs has an opposite effect. Our minimal advection-diffusion model and spatial correlation analyses correlate these dynamics to structure, with motor antagonism suppressing reconfiguration and demixing, while crosslinking enhances clustering. Despite the rich formulation space and emergent formulation-dependent structures, the nonequilibrium dynamics across all composites and timescales can be organized into three classes-slow isotropic reorientation, fast directional flow, and multimode restructuring. Moreover, our mathematical model demonstrates that diverse structural motifs can arise simply from the interplay between motor-driven advection and frictional drag. These general features of our platform facilitate applicability to other active matter systems and shed light on diverse ways that cytoskeletal components can cooperate or compete to enable wide-ranging cellular processes.

Constraint dependence of pressure on a passive probe in an active bath

Mechanical pressure in active matter is generally not a state variable and possesses abnormal properties, in stark contrast to equlibrium systems. We here show that the pressure on a passive probe exerted by an active fluid even depends on external constraints on the probe by means of simulation and theory, implying that the mechanical pressure is not an intrinsic physical quantity of active systems. The active mechanical pressure on the passive probe significantly increases and saturates as its elastic constraint (realized by a trap potential) or kinematic constraint (realized by environmental friction) strengthens. The microscopic origin for the constraint-dependent pressure is that the constraints influence the probe dynamics, and hence change the frequency and intensity of the collisions between the probe and active particles. Our findings not only greatly advance the understanding of active mechanical pressure but also provide a new way to in situ tune it.

Entropy by Neighbor Distance as a New Measure for Characterizing Spatiotemporal Orders in Microscopic Collective Systems

Collective systems self-organize to form globally ordered spatiotemporal patterns. Finding appropriate measures to characterize the order in these patterns will contribute to our understanding of the principles of self-organization in all collective systems. Here we examine a new measure based on the entropy of the neighbor distance distributions in the characterization of collective patterns. We study three types of systems: a simulated self-propelled boid system, two active colloidal systems, and one centimeter-scale robotic swarm system. In all these systems, the new measure proves sensitive in revealing active phase transitions and in distinguishing steady states. We envision that the entropy by neighbor distance could be useful for characterizing biological swarms such as bird flocks and for designing robotic swarms.

Emergent programmable behavior and chaos in dynamically driven active filaments

How the behavior of cells emerges from their constituent subcellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. The dynamics of this cell neck is powered by a coat of cilia across its length and tip. How a cell can program this active filamentous structure to produce desirable behaviors like search and homing to a target remains unknown. Here, we present an active filament model that allows us to uncover how a "program" (time sequence of active forcing) leads to "behavior" (filament shape dynamics). Our model captures two key features of this system-time-varying activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry-a "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic dynamics over long times. We further show that aperiodicity occurs due to a transition to chaos in regions of a biologically accessible parameter space. We also identify a simple nonlinear iterated map of filament shape that approximately predicts long-term behavior suggesting simple, artificial "programs" for filament functions such as homing and searching space. Last, we directly measure the statistical properties of biological programs in L. olor, enabling comparisons between model predictions and experiments.

Bio-enabled Engineering of Multifunctional "Living" Surfaces

Through the magic of "active matter"─matter that converts chemical energy into mechanical work to drive emergent properties─biology solves a myriad of seemingly enormous physical challenges. Using active matter surfaces, for example, our lungs clear an astronomically large number of particulate contaminants that accompany each of the 10,000 L of air we respire per day, thus ensuring that the lungs' gas exchange surfaces remain functional. In this Perspective, we describe our efforts to engineer artificial active surfaces that mimic active matter surfaces in biology. Specifically, we seek to assemble the basic active matter components─mechanical motor, driven constituent, and energy source─to design surfaces that support the continuous operation of molecular sensing, recognition, and exchange. The successful realization of this technology would generate multifunctional, "living" surfaces that combine the dynamic programmability of active matter and the molecular specificity of biological surfaces and apply them to applications in biosensors, chemical diagnostics, and other surface transport and catalytic processes. We describe our recent efforts in bio-enabled engineering of living surfaces through the design of molecular probes to understand and integrate native biological membranes into synthetic materials.

Active Colloids as Models, Materials, and Machines

Active colloids use energy input at the particle level to propel persistent motion and direct dynamic assemblies. We consider three types of colloids animated by chemical reactions, time-varying magnetic fields, and electric currents. For each type, we review the basic propulsion mechanisms at the particle level and discuss their consequences for collective behaviors in particle ensembles. These microscopic systems provide useful experimental models of nonequilibrium many-body physics in which dissipative currents break time-reversal symmetry. Freed from the constraints of thermodynamic equilibrium, active colloids assemble to form materials that move, reconfigure, heal, and adapt. Colloidal machines based on engineered particles and their assemblies provide a basis for mobile robots with increasing levels of autonomy. This review provides a conceptual framework for understanding and applying active colloids to create material systems that mimic the functions of living matter. We highlight opportunities for chemical engineers to contribute to this growing field.

Hydrodynamic interactions between squirmers near walls: far-field dynamics and near-field cluster stability

Confinement increases contacts between microswimmers in dilute suspensions and affects their interactions. In particular, boundaries have been shown experimentally to lead to the formation of clusters that would not occur in bulk fluids. To what extent does hydrodynamics govern these boundary-driven encounters between microswimmers? We consider theoretically the symmetric boundary-mediated encounters of model microswimmers under gravity through far-field interaction of a pair of weak squirmers, as well as the lubrication interactions occurring after contact between two or more squirmers. In the far field, the orientation of microswimmers is controlled by the wall and the squirming parameter. The presence of a second swimmer influences the orientation of the original squirmer, but for weak squirmers, most of the interaction occurs after contact. We thus analyse next the near-field reorientation of circular groups of squirmers. We show that a large number of swimmers and the presence of gravity can stabilize clusters of pullers, while the opposite is true for pushers; to be stable, clusters of pushers thus need to be governed by other interactions (e.g. phoretic). This simplified approach to the phenomenon of active clustering enables us to highlight the hydrodynamic contribution, which can be hard to isolate in experimental realizations.

Light, Matter, Action: Shining Light on Active Matter

Light carries energy and momentum. It can therefore alter the motion of objects on the atomic to astronomical scales. Being widely available, readily controllable, and broadly biocompatible, light is also an ideal tool to propel microscopic particles, drive them out of thermodynamic equilibrium, and make them active. Thus, light-driven particles have become a recent focus of research in the field of soft active matter. In this Perspective, we discuss recent advances in the control of soft active matter with light, which has mainly been achieved using light intensity. We also highlight some first attempts to utilize light's additional properties, such as its wavelength, polarization, and momentum. We then argue that fully exploiting light with all of its properties will play a critical role in increasing the level of control over the actuation of active matter as well as the flow of light itself through it. This enabling step will advance the design of soft active matter systems, their functionalities, and their transfer toward technological applications.

How to derive a predictive field theory for active Brownian particles: a step-by-step tutorial

The study of active soft matter has developed into one of the most rapidly growing areas of physics. Field theories, which can be developed either via phenomenological considerations or by coarse-graining of a microscopic model, are a very useful tool for understanding active systems. Here, we provide a detailed review of a particular coarse-graining procedure, theinteraction-expansion method(IEM). The IEM allows for the systematic microscopic derivation of predictive field theories for systems of interacting active particles. We explain in detail how it can be used for a microscopic derivation of active model B+, which is a widely used scalar active matter model. Extensions and possible future applications are also discussed.

Mechanical theory of nonequilibrium coexistence and motility-induced phase separation

Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both nonequilibrium and equilibrium systems. Here, we present a general mechanical theory for phase separation rooted in ideas explored nearly a half-century ago in the study of inhomogeneous fluids. The core idea is that the mechanical forces within the interface separating two coexisting phases uniquely determine coexistence criteria, regardless of whether a system is in equilibrium or not. We demonstrate the power and utility of this theory by applying it to active Brownian particles, predicting a quantitative phase diagram for motility-induced phase separation in both two and three dimensions. This formulation additionally allows for the prediction of novel interfacial phenomena, such as an increasing interface width while moving deeper into the two-phase region, a uniquely nonequilibrium effect confirmed by computer simulations. The self-consistent determination of bulk phase behavior and interfacial phenomena offered by this mechanical perspective provide a concrete path forward toward a general theory for nonequilibrium phase transitions.

Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids

Microtubule-based active fluids exhibit turbulent-like autonomous flows, which are driven by the molecular motor powered motion of filamentous constituents. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal patterning of the active stress controls the evolution of the ubiquitous bend instability of extensile active fluids and determines its critical length dependence. Combining optically controlled clusters with conventional kinesin motors enables one-time switching from contractile to extensile active stresses. These results open a path towards real-time control of the autonomous flows generated by active fluids.

Dynamics of active particles with translational and rotational inertia

Inertial effects affecting both the translational and rotational dynamics are inherent to a broad range of active systems at the macroscopic scale. Thus, there is a pivotal need for proper models in the framework of active matter to correctly reproduce experimental results, hopefully achieving theoretical insights. For this purpose, we propose an inertial version of the active Ornstein-Uhlenbeck particle (AOUP) model accounting for particle mass (translational inertia) as well as its moment of inertia (rotational inertia) and derive the full expression for its steady-state properties. The inertial AOUP dynamics introduced in this paper is designed to capture the basic features of the well-established inertial active Brownian particle model, i.e. the persistence time of the active motion and the long-time diffusion coefficient. For a small or moderate rotational inertia, these two models predict similar dynamics at all timescales and, in general, our inertial AOUP model consistently yields the same trend upon changing the moment of inertia for various dynamical correlation functions.

Three-Dimensionally Complex Phase Behavior and Collective Phenomena in Mixtures of Acoustically Powered Chiral Microspinners

The process of dynamic self-organization of small building blocks is fundamental to the emergent function of living systems and is characteristic of their out-of-equilibrium homeostasis. The ability to control the interactions of synthetic particles in large groups could lead to the realization of analogous macroscopic robotic systems with microscopic complexity. Rotationally induced self-organization has been observed in biological systems and modeled theoretically, but studies of fast, autonomously moving synthetic rotors remain rare. Here, we report switchable, out-of-equilibrium hydrodynamic assembly and phase separation in suspensions of acoustically powered chiral microspinners. Semiquantitative modeling suggests that three-dimensionally (3D) complex spinners interact through viscous and weakly inertial (streaming) flows. The interactions between spinners were studied over a range of densities to construct a phase diagram, which included gaseous dimer pairing at low density, collective rotation and multiphase separation at intermediate densities, and ultimately jamming at high density. The 3D chirality of the spinners leads to self-organization in parallel planes, forming a three-dimensionally hierarchical system that goes beyond the 2D systems that have so far been modeled computationally. Dense mixtures of spinners and passive tracer particles also show active-passive phase separation. These observations are consistent with recent theoretical predictions of the hydrodynamic coupling between rotlets generated by autonomous spinners and provide an exciting experimental window to the study of colloidal active matter and microrobotic systems.

Non-reciprocity induces resonances in a two-field Cahn-Hilliard model

We consider a non-reciprocally coupled two-field Cahn-Hilliard system that has been shown to allow for oscillatory behaviour and suppression of coarsening. After introducing the model, we first review the linear stability of steady uniform states and show that all instability thresholds are identical to the ones for a corresponding two-species reaction-diffusion system. Next, we consider a specific interaction of linear modes-a 'Hopf-Turing' resonance-and derive the corresponding amplitude equations using a weakly nonlinear approach. We discuss the weakly nonlinear results and finally compare them with fully nonlinear simulations for a specific conserved amended FitzHugh-Nagumo system. We conclude with a discussion of the limitations of the employed weakly nonlinear approach. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Dissipation and energy propagation across scales in an active cytoskeletal material

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system's total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system's total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

Active BiVO4 Swimmers Propelled by Depletion Gradients Caused by Photodeposition

Artificial active matter often self-propels by creating gradients of one or more species or quantities. For chemical swimmers, most frequently either O₂ or H⁺ that are created in certain catalytic reactions are causing the interfacial flows which drive the self-propulsion. While the palette of reactions is extending constantly, especially toward more bio-compatible fuels, the depletion of species is often overlooked. Here, the photodeposition of metal species on BiVO₄ micro swimmers is considered. During the photodeposition reaction, metal ions are removed from the solution creating a depleted region around the particle. The ability of this depletion to drive active motion of artificial micro swimmers, as well as the influences of different metal ions and counter ions on the motion are investigated and cross compared.

Collective response to local perturbations: how to evade threats without losing coherence

Living groups move in complex environments and are constantly subject to external stimuli, predatory attacks and disturbances. An efficient response to such perturbations is vital to maintain the group's coherence and cohesion. Perturbations are often local, i.e. they are initially perceived only by few individuals in the group, but can elicit a global response. This is the case of starling flocks, that can turn very quickly to evade predators. In this paper, we investigate the conditions under which a global change of direction can occur upon local perturbations. Using minimal models of self-propelled particles, we show that a collective directional response occurs on timescales that grow with the system size and it is, therefore, a finite-size effect. The larger the group is, the longer it will take to turn. We also show that global coherent turns can only take place if i) the mechanism for information propagation is efficient enough to transmit the local reaction undamped through the whole group; and if ii) motility is not too strong, to avoid that the perturbed individual leaves the group before the turn is complete. No compliance with such conditions results in the group's fragmentation or in a non-efficient response.

Self-propelling colloids with finite state dynamics

Endowing materials with the ability to sense, adapt, and respond to stimuli holds the key to a progress leap in autonomous systems. In spite of the growing success of macroscopic soft robotic devices, transferring these concepts to the microscale presents several challenges connected to the lack of suitable fabrication and design techniques and of internal response schemes that connect the materials' properties to the function of the active units. Here, we realize self-propelling colloidal clusters which possess a finite number of internal states, which define their motility and which are connected by reversible transitions. We produce these units via capillary assembly combining hard polystyrene colloids with two different types of thermoresponsive microgels. The clusters, actuated by spatially uniform AC electric fields, adapt their shape and dielectric properties, and consequently their propulsion, via reversible temperature-induced transitions controlled by light. The different transition temperatures for the two microgels enable three distinct dynamical states corresponding to three illumination intensity levels. The sequential reconfiguration of the microgels affects the velocity and shape of the active trajectories according to a pathway defined by tailoring the clusters' geometry during assembly. The demonstration of these simple systems indicates an exciting route toward building more complex units with broader reconfiguration schemes and multiple responses as a step forward in the pursuit of adaptive autonomous systems at the colloidal scale.

Colloidal Active Matter Mimics the Behavior of Biological Microorganisms-An Overview

This article provides a review of the recent development of biomimicking behaviors in active colloids. While the behavior of biological microswimmers is undoubtedly influenced by physics, it is frequently guided and manipulated by active sensing processes. Understanding the respective influences of the surrounding environment can help to engineering the desired response also in artificial swimmers. More often than not, the achievement of biomimicking behavior requires the understanding of both biological and artificial microswimmers swimming mechanisms and the parameters inducing mechanosensory responses. The comparison of both classes of microswimmers provides with analogies in their dependence on fuels, interaction with boundaries and stimuli induced motion, or taxis.

Learning hydrodynamic equations for active matter from particle simulations and experiments

Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In parallel, data-driven algorithms for learning interpretable continuum models have shown promising potential for the recovery of underlying partial differential equations (PDEs) from continuum simulation data. By contrast, learning macroscopic hydrodynamic equations for active matter directly from experiments or particle simulations remains a major challenge, especially when continuum models are not known a priori or analytic coarse graining fails, as often is the case for nondilute and heterogeneous systems. Here, we present a framework that leverages spectral basis representations and sparse regression algorithms to discover PDE models from microscopic simulation and experimental data, while incorporating the relevant physical symmetries. We illustrate the practical potential through a range of applications, from a chiral active particle model mimicking nonidentical swimming cells to recent microroller experiments and schooling fish. In all these cases, our scheme learns hydrodynamic equations that reproduce the self-organized collective dynamics observed in the simulations and experiments. This inference framework makes it possible to measure a large number of hydrodynamic parameters in parallel and directly from video data.

Motor processivity and speed determine structure and dynamics of microtubule-motor assemblies

Active matter systems can generate highly ordered structures, avoiding equilibrium through the consumption of energy by individual constituents. How the microscopic parameters that characterize the active agents are translated to the observed mesoscopic properties of the assembly has remained an open question. These active systems are prevalent in living matter; for example, in cells, the cytoskeleton is organized into structures such as the mitotic spindle through the coordinated activity of many motor proteins walking along microtubules. Here, we investigate how the microscopic motor-microtubule interactions affect the coherent structures formed in a reconstituted motor-microtubule system. This question is of deeper evolutionary significance as we suspect motor and microtubule type contribute to the shape and size of resulting structures. We explore key parameters experimentally and theoretically, using a variety of motors with different speeds, processivities, and directionalities. We demonstrate that aster size depends on the motor used to create the aster, and develop a model for the distribution of motors and microtubules in steady-state asters that depends on parameters related to motor speed and processivity. Further, we show that network contraction rates scale linearly with the single-motor speed in quasi-one-dimensional contraction experiments. In all, this theoretical and experimental work helps elucidate how microscopic motor properties are translated to the much larger scale of collective motor-microtubule assemblies.

Collective Behaviors of Active Matter Learning from Natural Taxes Across Scales

Taxis orientation is common in microorganisms, and it provides feasible strategies to operate active colloids as small-scale robots. Collective taxes involve numerous units that collectively perform taxis motion, whereby the collective cooperation between individuals enables the group to perform efficiently, adaptively, and robustly. Hence, analyzing and designing collectives is crucial for developing and advancing microswarm toward practical or clinical applications. In this review, natural taxis behaviors are categorized and synthetic microrobotic collectives are discussed as bio-inspired realizations, aiming at closing the gap between taxis strategies of living creatures and those of functional active microswarms. As collective behaviors emerge within a group, the global taxis to external stimuli guides the group to conduct overall tasks, whereas the local taxis between individuals induces synchronization and global patterns. By encoding the local orientations and programming the global stimuli, various paradigms can be introduced for coordinating and controlling such collective microrobots, from the viewpoints of fundamental science and practical applications. Therefore, by discussing the key points and difficulties associated with collective taxes of different paradigms, this review potentially offers insights into mimicking natural collective behaviors and constructing intelligent microrobotic systems for on-demand control and preassigned tasks.

Narrow Pore Crossing of Active Particles under Stochastic Resetting

We propose a two-dimensional model of biochemical activation process, whereby self-propelling particles of finite correlation times are injected at the center of a circular cavity with constant rate equal to the inverse of their lifetime; activation is triggered when one such particle hits a receptor on the cavity boundary, modeled as a narrow pore. We numerically investigated this process by computing the particle mean-first exit times through the cavity pore as a function of the correlation and injection time constants. Due to the breach of the circular symmetry associated with the positioning of the receptor, the exit times may depend on the orientation of the self-propelling velocity at injection. Stochastic resetting appears to favor activation for large particle correlation times, where most of the underlying diffusion process occurs at the cavity boundary.

Collective rotational motion of freely expanding T84 epithelial cell colonies

Coordinated rotational motion is an intriguing, yet still elusive mode of collective cell migration, which is relevant in pathological and morphogenetic processes. Most of the studies on this topic have been carried out on epithelial cells plated on micropatterned substrates, where cell motion is confined in regions of well-defined shapes coated with extracellular matrix adhesive proteins. The driver of collective rotation in such conditions has not been clearly elucidated, although it has been speculated that spatial confinement can play an essential role in triggering cell rotation. Here, we study the growth of epithelial cell colonies freely expanding (i.e. with no physical constraints) on the surface of cell culture plates and focus on collective cell rotation in such conditions, a case which has received scarce attention in the literature. One of the main findings of our work is that coordinated cell rotation spontaneously occurs in cell clusters in the free growth regime, thus implying that cell confinement is not necessary to elicit collective rotation as previously suggested. The extent of collective rotation was size and shape dependent: a highly coordinated disc-like rotation was found in small cell clusters with a round shape, while collective rotation was suppressed in large irregular cell clusters generated by merging of different clusters in the course of their growth. The angular motion was persistent in the same direction, although clockwise and anticlockwise rotations were equally likely to occur among different cell clusters. Radial cell velocity was quite low as compared to the angular velocity, in agreement with the free expansion regime where cluster growth is essentially governed by cell proliferation. A clear difference in morphology was observed between cells at the periphery and the ones in the core of the clusters, the former being more elongated and spread out as compared to the latter. Overall, our results, to our knowledge, provide the first quantitative and systematic evidence that coordinated cell rotation does not require a spatial confinement and occurs spontaneously in freely expanding epithelial cell colonies, possibly as a mechanism for the system.

Oil-on-water droplets faceted and stabilized by vortex halos in the subphase

For almost 200 y, the dominant approach to understand oil-on-water droplet shape and stability has been the thermodynamic expectation of minimized energy, yet parallel literature shows the prominence of Marangoni flow, an adaptive gradient of interfacial tension that produces convection rolls in the water. Our experiments, scaling arguments, and linear stability analysis show that the resulting Marangoni-driven high-Reynolds-number flow in shallow water overcomes radial symmetry of droplet shape otherwise enforced by the Laplace pressure. As a consequence, oil-on-water droplets are sheared to become polygons with distinct edges and corners. Moreover, subphase flows beneath individual droplets can inhibit the coalescence of adjacent droplets, leading to rich many-body dynamics that makes them look alive. The phenomenon of a "vortex halo" in the liquid subphase emerges as a hidden variable.

On Nanomachines and Their Future Perspectives in Biomedicine

Nano/micromotors are a class of active matter that can self-propel converting different types of input energy into kinetic energy. The huge efforts that are made in this field over the last years result in remarkable advances. Specifically, a high number of publications have dealt with biomedical applications that these motors may offer. From the first attempts in 2D cell cultures, the research has evolved to tissue and in vivo experimentation, where motors show promising results. In this Perspective, an overview over the evolution of motors with focus on bio-relevant environments is provided. Then, a discussion on the advances and challenges is presented, and eventually some remarks and perspectives of the field are outlined.

Chloroplasts in plant cells show active glassy behavior under low-light conditions

Plants have developed intricate mechanisms to adapt to changing light conditions. Besides phototropism and heliotropism (differential growth toward light and diurnal motion with respect to sunlight, respectively), chloroplast motion acts as a fast mechanism to change the intracellular structure of leaf cells. While chloroplasts move toward the sides of the plant cell to avoid strong light, they accumulate and spread out into a layer on the bottom of the cell at low light to increase the light absorption efficiency. Although the motion of chloroplasts has been studied for over a century, the collective organelle motion leading to light-adapting self-organized structures remains elusive. Here, we study the active motion of chloroplasts under dim-light conditions, leading to an accumulation in a densely packed quasi-2D layer. We observe burst-like rearrangements and show that these dynamics resemble systems close to the glass transition by tracking individual chloroplasts. Furthermore, we provide a minimal mathematical model to uncover relevant system parameters controlling the stability of the dense configuration of chloroplasts. Our study suggests that the meta-stable caging close to the glass transition in the chloroplast monolayer serves a physiological relevance: Chloroplasts remain in a spread-out configuration to increase the light uptake but can easily fluidize when the activity is increased to efficiently rearrange the structure toward an avoidance state. Our research opens questions about the role that dynamical phase transitions could play in self-organized intracellular responses of plant cells toward environmental cues.

Active morphogenesis of patterned epithelial shells

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.

Understanding the Feedback Loops between Energy, Matter and Life

This review gathers recent findings in biophysics that shed light on the biological principle of self-organization, spanning from molecules to more complicated systems with higher information processing capacity. The focus is on "feedback loops" from information and matter to an exchange component with a more fundamental meaning than "cybernetic regulation" and "maintenance of homeostasis". This article proposes that electric and electromagnetic forces are the most important mediators over large distances. Field-like mediation is distinguished from cell-to-cell communication by special electric- or ion-guiding mechanisms that create additional pathways to the "classical" mediators such as nerve conduction or blood flow. Resonance phenomena from phonons and photons in the visible range will be discussed in relation to organelles, cytoskeletal elements and molecules. In this context, the aqueous surrounding of molecules and cells is an important aspect. Many of these phenomena are caused by quantum physics, such as the tunneling of electrons in enzymes or in other coherent working systems. This suggests that quantum information processing is also spread over large-scale areas of an organism.

Ray Optics for Gliders

Control of self-propelled particles is central to the development of many microrobotic technologies, from dynamically reconfigurable materials to advanced lab-on-a-chip systems. However, there are few physical principles by which particle trajectories can be specified and can be used to generate a wide range of behaviors. Within the field of ray optics, a single principle for controlling the trajectory of light─Snell's law─yields an intuitive framework for engineering a broad range of devices, from microscopes to cameras and telescopes. Here we show that the motion of self-propelled particles gliding across a resistance discontinuity is governed by a variant of Snell's law, and develop a corresponding ray optics for gliders. Just as the ratio of refractive indexes sets the path of a light ray, the ratio of resistance coefficients is shown to determine the trajectories of gliders. The magnitude of refraction depends on the glider's shape, in particular its aspect ratio, which serves as an analogue to the wavelength of light. This enables the demixing of a polymorphic, many-shaped, beam of gliders into distinct monomorphic, single-shaped, beams through a friction prism. In turn, beams of monomorphic gliders can be focused by spherical and gradient friction lenses. Alternatively, the critical angle for total internal reflection can be used to create shape-selective glider traps. Overall our work suggests that furthering the analogy between light and microscopic gliders may be used for sorting, concentrating, and analyzing self-propelled particles.

Durability of Aligned Microtubules Dependent on Persistence Length Determines Phase Transition and Pattern Formation in Collective Motion

Collective motion is a ubiquitous phenomenon in nature. The collective motion of cytoskeleton filaments results mainly from dynamic collisions and alignments; however, the detailed mechanism of pattern formation still needs to be clarified. In particular, the influence of persistence length, which is a measure of filament flexibility, on collective motion is still unclear and lacks experimental verifications although it is likely to directly affect the orientational flexibility of filaments. Here, we investigated the collective motion of microtubules with different persistence lengths using a microtubule-kinesin motility system. We showed that local interactions between microtubules significantly vary depending on their persistence length. We demonstrated that the bundling of microtubules is enhanced by more durable alignment, rather than by greater likelihood of alignment. An agent-based computational model confirmed that the rigidity-dependent durability of microtubule alignment dominates their collective behavior.

Geometric and Scaling Effects in the Speed of Catalytic Enzyme Micropumps

Self-powered, biocompatible pumps in the nanometer to micron length scale have the potential to enable technology in several fields, including chemical analysis and medical diagnostics. Chemically powered, catalytic micropumps have been developed but are not able to function well in biocompatible environments due to their intolerance of salt solutions and the use of toxic fuels. In contrast, enzymatically powered catalytic pumps offer good biocompatibility, selectivity, and scalability, but their performance at length scales below a few millimeters, which is important to many of their possible applications, has not been well tested. Here, urease-based enzyme pumps of millimeter and micrometer dimensions were fabricated and studied. The scaling of the pumping velocity was measured experimentally and simulated by numerical modeling. Pumping speeds were analyzed accurately by eliminating Brownian noise from the data using enzyme patches between 5 mm and 350 μm in size. Pumping speeds of microns per second could be achieved with urease pumps and were fastest when the channel height exceeded the width of the catalytic pump patch. In all cases, pumping was weak when the dimensions of the patch were 100 μm or less. Experimental and simulation results were consistent with a density-driven pumping mechanism at all sizes studied and served as a framework for the in silico study of more complex two-dimensional (2D) and three-dimensional (3D) geometries. Attempts to create directional flow by juxtaposing inward and outward pumps were unsuccessful because of the symmetry of convection rolls produced by millimeter-size pump patches and the slow speeds of smaller pumps. However, simulations of a corrugated ratchet structure showed that directional pumping could be achieved with pump patches in the millimeter size range.

Optimal transport and control of active drops

Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural "gather-move-spread" strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

Encapsulated bacteria deform lipid vesicles into flagellated swimmers

Swimming bacterial pathogens can penetrate and shape the membranes of their host cells. We study an artificial model system of this kind comprising Escherichia coli enclosed inside vesicles, which consist of nothing more than a spherical membrane bag. The bacteria push out membrane tubes, and the tubes propel the vesicles. This phenomenon is intriguing because motion cannot be generated by pushing the vesicles from within. We explain the motility of our artificial cell by a shape coupling between the flagella of each bacterium and the enclosing membrane tube. This constitutes a design principle for conferring motility to cell-sized vesicles and demonstrates the universality of lipid membranes as a building block in the development of new biohybrid systems.

We study a synthetic system of motile Escherichia coli bacteria encapsulated inside giant lipid vesicles. Forces exerted by the bacteria on the inner side of the membrane are sufficient to extrude membrane tubes filled with one or several bacteria. We show that a physical coupling between the membrane tube and the flagella of the enclosed cells transforms the tube into an effective helical flagellum propelling the vesicle. We develop a simple theoretical model to estimate the propulsive force from the speed of the vesicles and demonstrate the good efficiency of this coupling mechanism. Together, these results point to design principles for conferring motility to synthetic cells.