Curvature-Guided Motility of Microalgae in Geometric Confinement

Experimental and numerical study of a second-order transition in the behavior of confined self-propelled particles

In this paper, we conduct experimental investigations on the behavior of confined self-propelled particles within a circular arena, employing small commercial robots capable of locomotion, communication, and information processing. These robots execute circular trajectories, which can be clockwise or counterclockwise, based on two internal states. Using a majority-based stochastic decision algorithm, each robot can reverse its direction based on the states of two neighboring robots. By manipulating a control parameter governing the interaction, the system exhibits a transition from a state where all robots rotate randomly to one where they rotate uniformly in the same direction. Moreover, this transition significantly impacts the trajectories of the robots. To extend our findings to larger systems, we introduce a mathematical model enabling characterization of the order transition type and the resulting trajectories. Our results reveal a second-order transition from active Brownian to chiral motion.

Polar order, shear banding, and clustering in confined active matter

We investigate the collective behavior of sterically interacting self-propelled particles confined in a harmonic potential. Our theoretical and numerical study unveils the emergence of distinctive collective polar organizations, revealing how different levels of interparticle torques and noise influence the system. The observed phases include the shear-banded vortex, where the system self organizes in two concentric bands rotating in opposite directions around the potential center; the uniform vortex, where the two bands merge into a close packed configuration rotating uniformly as a quasi-rigid body; and the orbiting polar state, characterized by parallel orientation vectors and the cluster revolving around the potential center, without rotation, as a rigid body. Intriguingly, at lower filling fractions, the vortex and polar phases merge into a single phase where the trapped cluster breaks into smaller polarized clusters, each one orbiting the potential center as a rigid body.

Stationary particle currents in sedimenting active matter wetting a wall

Recently it was predicted, on the basis of a lattice gas model, that scalar active matter in a gravitational field would rise against gravity up a confining wall or inside a thin capillary-in spite of repulsive particle-wall interactions [Phys. Rev. Lett. 124, 048001 (2020)0031-900710.1103/PhysRevLett.124.048001]. In this paper we confirm this prediction with sedimenting active Brownian particles (ABPs) in a box numerically and elucidate the mechanism leading to the formation of a meniscus rising above the bulk of the sedimentation region. The height of the meniscus increases with the activity of the system, algebraically with the Péclet number. The formation of the meniscus is determined by a stationary circular particle current, a vortex, centered at the base of the meniscus, whose size and strength increase with the ABP activity. The origin of these vortices can be traced back to the confinement of the ABPs in a box: already the stationary state of ideal (noninteracting) ABPs without gravitation displays circular currents that arrange in a highly symmetric way in the eight octants of the box. Gravitation distorts this vortex configuration downward, leaving two major vortices at the two side walls, with a strong downward flow along the walls. Repulsive interactions between the ABPs change this situation only as soon as motility induced phase separation (MIPS) sets in and forms a dense, sedimented liquid region at the bottom, which pushes the center of the vortex upwards towards the liquid-gas interface. Self-propelled particles therefore represent an impressive realization of scalar active matter that forms stationary particle currents being able to perform visible work against gravity or any other external field, which we predict to be observable experimentally in active colloids under gravitation.

Methods and Measures for Investigating Microscale Motility

Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks, and theoretical methods, we can begin to probe the complex lives of microscopic motile organisms and answer the intertwining biological and physical questions of how these diverse lifeforms navigate their surroundings. Herein, we summarize the main mechanisms of microscale motility and give an overview of different experimental, analytical, and mathematical methods used to study them across different scales encompassing the molecular-, individual-, to population-level. We identify transferable techniques, pressing challenges, and future directions in the field. This review can serve as a starting point for researchers who are interested in exploring and quantifying the movements of organisms in the microscale world.

Kinetic temperature and pressure of an active Tonks gas

Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions.

Dispersion of run-and-tumble microswimmers through disordered media

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of noninteracting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function f(ϕ,Pe) of the obstacle area fraction ϕ and Péclet number Pe, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media (Peϕ≪1), and its extension to denser media is obtained using stochastic simulations. As we explain, the model is also easily generalized to describe dispersion in three dimensions.

Noise-induced escape of a self-propelled particle from metastable orbits

Active particles, like motile microorganisms and active colloids, are often found in confined environments where they can be arrested in a persistent orbital motion. Here, we investigate noise-induced switching between different coexisting orbits of a confined active particle as a stochastic escape problem. We show that, in the low-noise regime, this problem can be formulated as a least-action principle, which amounts to finding the most probable escape path from an orbit to the basin of attraction of another coexisting orbit. The corresponding action integral coincides with the activation energy, a quantity readily accessible in experiments and simulations via escape rate data. To illustrate how this approach can be used to tackle specific problems, we calculate optimum escape paths and activation energies for noise-induced transitions between clockwise and counterclockwise circular orbits of an active particle in radially symmetric confinement. We also investigated transitions between orbits of different topologies (ovals and lemniscates) coexisting in elliptic confinement. In all worked examples, the calculated optimum paths and minimum actions are in excellent agreement with mean-escape-time data obtained from direct numerical integration of the Langevin equations.

Spatial Distribution of Flagellated Microalgae Chlamydomonas reinhardtii in a Quasi-Two-Dimensional Space

Although the phenomenon of collective order formation by cell-cell interactions in motile cells, microswimmers, has been a topic of interest, most studies have been conducted under conditions of high cell density, where the space occupancy of a cell population relative to the space size ϕ>0.1 (ϕ is the area fraction). We experimentally determined the spatial distribution (SD) of the flagellated unicellular green alga Chlamydomonas reinhardtii at a low cell density (ϕ≈0.01) in a quasi-two-dimensional (thickness equal to cell diameter) restricted space and used the variance-to-mean ratio to investigate the deviation from the random distribution of cells, that is, do cells tend to cluster together or avoid each other? The experimental SD is consistent with that obtained by Monte Carlo simulation, in which only the excluded volume effect (EV effect) due to the finite size of cells is taken into account, indicating that there is no interaction between cells other than the EV effect at a low cell density of ϕ≈0.01. A simple method for fabricating a quasi-two-dimensional space using shim rings was also proposed.

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Light-regulated adsorption and desorption of Chlamydomonas cells at surfaces

Microbial colonization of surfaces represents the first step towards biofilm formation, which is a recurring phenomenon in nature with beneficial and detrimental implications in technological and medical settings. Consequently, there is interest in elucidating the fundamental aspects of the initial stages of biofilm formation of microorganisms on solid surfaces. While most of the research is oriented to understand bacterial surface colonization, the fundamental principles of surface colonization of motile, photosynthetic microbes remain largely unexplored so far. Recent single-cell studies showed that the flagellar adhesion of Chlamydomonas reinhardtii is switched on in blue light and switched off under red light [Kreis et al., Nat. Phys., 2018, 14, 45-49]. Here, we study this light-switchable surface association on the population level and measure the kinetics of adsorption and desorption of suspensions of motile C. reinhardtii cells on glass surfaces using bright-field optical microscopy. We observe that both processes exhibit a response lag relative to the time at which the blue- and red-light conditions are set and model this feature using time-delayed Langmuir-type kinetics. We find that cell adsorption occurs significantly faster than desorption, which we attribute to the protein-mediated molecular adhesion mechanism of the cells. Adsorption experiments using phototactically blind C. reinhardtii mutants demonstrate that phototaxis does not affect the cell adsorption kinetics. Hence, this framework can be used as an assay for characterizing the dynamics of the surface colonization of microbial species exhibiting light-regulated surface adhesion under precisely controlled environmental conditions.

Squirmer hydrodynamics near a periodic surface topography

The behaviour of microscopic swimmers has previously been explored near large-scale confining geometries and in the presence of very small-scale surface roughness. Here, we consider an intermediate case of how a simple microswimmer, the tangential spherical squirmer, behaves adjacent to singly and doubly periodic sinusoidal surface topographies that spatially oscillate with an amplitude that is an order of magnitude less than the swimmer size and wavelengths that are also within an order of magnitude of this scale. The nearest neighbour regularised Stokeslet method is used for numerical explorations after validating its accuracy for a spherical tangential squirmer that swims stably near a flat surface. The same squirmer is then introduced to different surface topographies. The key governing factor in the resulting swimming behaviour is the size of the squirmer relative to the surface topography wavelength. For instance, directional guidance is not observed when the squirmer is much larger, or much smaller, than the surface topography wavelength. In contrast, once the squirmer size is on the scale of the topography wavelength, limited guidance is possible, often with local capture in the topography troughs. However, complex dynamics can also emerge, especially when the initial configuration is not close to alignment along topography troughs or above topography crests. In contrast to sensitivity in alignment and topography wavelength, reductions in the amplitude of the surface topography or variations in the shape of the periodic surface topography do not have extensive impacts on the squirmer behaviour. Our findings more generally highlight that the numerical framework provides an essential basis to elucidate how swimmers may be guided by surface topography.

Collective motion of active particles exhibiting non-reciprocal orientational interactions

We present a Brownian dynamics study of a 2D bath of active particles interacting among each other through usual steric interactions and, additionally, via non-reciprocal avoidant orientational interactions. We motivate them by the fact that the two flagella of the alga Chlamydomonas interact sterically with nearby surfaces such that a torque acts on the alga. As expected, in most cases such interactions disrupt the motility-induced particle clustering in active baths. Surprisingly, however, we find that the active particles can self-organize into collectively moving flocks if the range of non-reciprocal interactions is close to that of steric interactions. We observe that the flocking motion can manifest itself through a variety of structural forms, spanning from single dense bands to multiple moderately-dense stripes, which are highly dynamic. The flocking order parameter is found to be only weakly dependent on the underlying flock structure. Together with the variance of the local-density distribution, one can clearly group the flocking motion into the two separate band and dynamic-stripes states.

Switching of behavioral modes and their modulation by a geometrical cue in the ciliate Stentor coeruleus

Protists ubiquitously live in nature and play key roles in the food web chain. Their habitats consist of various geometrical structures, such as porous media and rigid surfaces, affecting their motilities. A kind of protist, Stentor coeruleus, exhibits free swimming and adhering for feeding. Under environmental and culture conditions, these organisms are often found in sediments with complex geometries. The determination of anchoring location is essential for their lives. However, the factors that induce the behavioral transition from swimming to adhering are still unknown. In this study, we quantitatively characterized the behavioral transitions in S. coeruleus and observed the behavior in a chamber with dead ends made by a simple structure mimicking the environmental structures. As a result, the cell adheres and feeds in narrow spaces between the structure and the chamber wall. It may be reasonable for the organism to hide itself from predators and capture prey in these spaces. The behavioral strategy for the exploration and exploitation of spaces with a wide variety of geometries in their habitats is discussed.

Sharp turns and gyrotaxis modulate surface accumulation of microorganisms

Populations of swimming microorganisms are ubiquitous in aqueous environments from blood vessels to oceans and from biofilms to biotechnological industries, where they routinely encounter solid boundaries. This paper explores experimentally how the presence of boundaries influences the behavior of a marine alga (Heterosigma akashiwo), whose normal trajectories exhibit both random sharp turns and gravitational reorientation (gyrotaxis). Proximity to a plane boundary strongly increases the probability of sharp turns and thereby influences the distributions of swimming speed, angular velocity and, unexpectedly, rotational diffusivity as functions of distance from the boundary and of swimming orientation. These variations all contribute to enhancing accumulation beneath an upper boundary much more than gyrotaxis alone.

The accumulation of swimming microorganisms at surfaces is an essential feature of various physical, chemical, and biological processes in confined spaces. To date, this accumulation is mainly assumed to depend on the change of swimming speed and angular velocity caused by cell-wall contact and hydrodynamic interaction. Here, we measured the swimming trajectories of Heterosigma akashiwo (a biflagellate marine alga) near vertical and horizontal rigid boundaries. We observed that the probability of sharp turns is greatly increased near a vertical wall, resulting in significant changes in the distributions of average swimming speed, angular velocity, and rotational diffusivity near the wall (a quantity that has not previously been investigated) as functions of both distance from the wall and swimming orientation. These cannot be satisfactorily explained by standard hydrodynamic models. Detailed examination of an individual cell trajectory shows that wall contact by the leading flagellum triggers complex changes in the behavior of both flagella that cannot be incorporated in a mechanistic model. Our individual-based model for predicting cell concentration using the measured distributions of swimming speed, angular velocity, and rotational diffusivity agrees well with the experiment. The experiments and model are repeated for a cell suspension in a vertical plane, bounded above by a horizontal wall. The cell accumulation beneath the wall, expected from gyrotaxis, is considerably amplified by cell-wall interaction. These findings may shed light on the prediction and control of cell distribution mediated by gyrotaxis and cell-wall contact.

Anomalous Cooling and Overcooling of Active Colloids

The phenomenon that a system at a hot temperature cools faster than at a warm temperature, referred to as the Mpemba effect, has recently been realized for trapped colloids. Here, we investigate the cooling and heating process of a self-propelled active colloid using numerical simulations and theoretical calculations with a model that can be directly tested in experiments. Upon cooling, activity induces a Mpemba effect and the active particle transiently escapes an effective temperature description. At the end of the cooling process the notion of temperature is recovered and the system can exhibit even smaller temperatures than its final temperature, a surprising phenomenon which we refer to as activity-induced overcooling.

Confinement-induced accumulation and de-mixing of microscopic active-passive mixtures

Understanding the out-of-equilibrium properties of noisy microscale systems and the extent to which they can be modulated externally, is a crucial scientific and technological challenge. It holds the promise to unlock disruptive new technologies ranging from targeted delivery of chemicals within the body to directed assembly of new materials. Here we focus on how active matter can be harnessed to transport passive microscopic systems in a statistically predictable way. Using a minimal active-passive system of weakly Brownian particles and swimming microalgae, we show that spatial confinement leads to a complex non-monotonic steady-state distribution of colloids, with a pronounced peak at the boundary. The particles’ emergent active dynamics is well captured by a space-dependent Poisson process resulting from the space-dependent motion of the algae. Based on our findings, we then realise experimentally the de-mixing of the active-passive suspension, opening the way for manipulating colloidal objects via controlled activity fields.

Understanding how order emerges in active matter may facilitate macroscopic control of microscopic objects. Here, Williams et al. show how to control the transport of passive microscopic particles in presence of motile algae in conjunction with boundary-induced accumulation of microswimmers.

Interplay of surface interaction and magnetic torque in single-cell motion of magnetotactic bacteria in microfluidic confinement

Swimming microorganisms often experience complex environments in their natural habitat. The same is true for microswimmers in envisioned biomedical applications. The simple aqueous conditions typically studied in the lab differ strongly from those found in these environments and often exclude the effects of small volume confinement or the influence that external fields have on their motion. In this work, we investigate magnetically steerable microswimmers, specifically magnetotactic bacteria, in strong spatial confinement and under the influence of an external magnetic field. We trap single cells in micrometer-sized microfluidic chambers and track and analyze their motion, which shows a variety of different trajectories, depending on the chamber size and the strength of the magnetic field. Combining these experimental observations with simulations using a variant of an active Brownian particle model, we explain the variety of trajectories by the interplay between the wall interactions and the magnetic torque. We also analyze the pronounced cell-to-cell heterogeneity, which makes single-cell tracking essential for an understanding of the motility patterns. In this way, our work establishes a basis for the analysis and prediction of microswimmer motility in more complex environments.

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.

Phenotyping single-cell motility in microfluidic confinement

The movement trajectories of organisms serve as dynamic read-outs of their behaviour and physiology. For microorganisms this can be difficult to resolve due to their small size and fast movement. Here, we devise a novel droplet microfluidics assay to encapsulate single micron-sized algae inside closed arenas, enabling ultralong high-speed tracking of the same cell. Comparing two model species - Chlamydomonas reinhardtii (freshwater, 2 cilia), and Pyramimonas octopus (marine, 8 cilia), we detail their highly-stereotyped yet contrasting swimming behaviours and environmental interactions. By measuring the rates and probabilities with which cells transition between a trio of motility states (smooth-forward swimming, quiescence, tumbling or excitable backward swimming), we reconstruct the control network that underlies this gait switching dynamics. A simplified model of cell-roaming in circular confinement reproduces the observed long-term behaviours and spatial fluxes, including novel boundary circulation behaviour. Finally, we establish an assay in which pairs of droplets are fused on demand, one containing a trapped cell with another containing a chemical that perturbs cellular excitability, to reveal how aneural microorganisms adapt their locomotor patterns in real-time.

Self-generated oxygen gradients control collective aggregation of photosynthetic microbes

For billions of years, photosynthetic microbes have evolved under the variable exposure to sunlight in diverse ecosystems and microhabitats all over our planet. Their abilities to dynamically respond to alterations of the luminous intensity, including phototaxis, surface association and diurnal cell cycles, are pivotal for their survival. If these strategies fail in the absence of light, the microbes can still sustain essential metabolic functionalities and motility by switching their energy production from photosynthesis to oxygen respiration. For suspensions of motile C. reinhardtii cells above a critical density, we demonstrate that this switch reversibly controls collective microbial aggregation. Aerobic respiration dominates over photosynthesis in conditions of low light, which causes the microbial motility to sensitively depend on the local availability of oxygen. For dense microbial populations in self-generated oxygen gradients, microfluidic experiments and continuum theory based on a reaction–diffusion mechanism show that oxygen-regulated motility enables the collective emergence of highly localized regions of high and low cell densities.

Strong confinement of active microalgae leads to inversion of vortex flow and enhanced mixing

Microorganisms swimming through viscous fluids imprint their propulsion mechanisms in the flow fields they generate. Extreme confinement of these swimmers between rigid boundaries often arises in natural and technological contexts, yet measurements of their mechanics in this regime are absent. Here, we show that strongly confining the microalga Chlamydomonas between two parallel plates not only inhibits its motility through contact friction with the walls but also leads, for purely mechanical reasons, to inversion of the surrounding vortex flows. Insights from the experiment lead to a simplified theoretical description of flow fields based on a quasi-2D Brinkman approximation to the Stokes equation rather than the usual method of images. We argue that this vortex flow inversion provides the advantage of enhanced fluid mixing despite higher friction. Overall, our results offer a comprehensive framework for analyzing the collective flows of strongly confined swimmers.

Mammalian sperm hyperactivation regulates navigation via physical boundaries and promotes pseudo-chemotaxis

Mammalian sperm migration within the complex and dynamic environment of the female reproductive tract toward the fertilization site requires navigational mechanisms, through which sperm respond to the tract environment and maintain the appropriate swimming behavior. In the oviduct (fallopian tube), sperm undergo a process called "hyperactivation," which involves switching from a nearly symmetrical, low-amplitude, and flagellar beating pattern to an asymmetrical, high-amplitude beating pattern that is required for fertilization in vivo. Here, exploring bovine sperm motion in high-aspect ratio microfluidic reservoirs as well as theoretical and computational modeling, we demonstrate that sperm hyperactivation, in response to pharmacological agonists, modulates sperm-sidewall interactions and thus navigation via physical boundaries. Prior to hyperactivation, sperm remained swimming along the sidewalls of the reservoirs; however, once hyperactivation caused the intrinsic curvature of sperm to exceed a critical value, swimming along the sidewalls was reduced. We further studied the effect of noise in the intrinsic curvature near the critical value and found that these nonthermal fluctuations yielded an interesting "Run-Stop" motion on the sidewall. Finally, we observed that hyperactivation produced a "pseudo-chemotaxis" behavior, in that sperm stayed longer within microfluidic chambers containing higher concentrations of hyperactivation agonists.

Emergent probability fluxes in confined microbial navigation

When the motion of a motile cell is observed closely, it appears erratic, and yet the combination of nonequilibrium forces and surfaces can produce striking examples of organization in microbial systems. While most of our current understanding is based on bulk systems or idealized geometries, it remains elusive how and at which length scale self-organization emerges in complex geometries. Here, using experiments and analytical and numerical calculations, we study the motion of motile cells under controlled microfluidic conditions and demonstrate that probability flux loops organize active motion, even at the level of a single cell exploring an isolated compartment of nontrivial geometry. By accounting for the interplay of activity and interfacial forces, we find that the boundary's curvature determines the nonequilibrium probability fluxes of the motion. We theoretically predict a universal relation between fluxes and global geometric properties that is directly confirmed by experiments. Our findings open the possibility to decipher the most probable trajectories of motile cells and may enable the design of geometries guiding their time-averaged motion.

Rebound and scattering of motile Chlamydomonas algae in confined chambers

Motivated by recent experiments demonstrating that motile algae get trapped in draining foams, we study the trajectories of microorganisms confined in model foam channels (section of a Plateau border). We track single Chlamydomonas reinhardtii cells confined in a thin three-circle microfluidic chamber and show that their spatial distribution exhibits strong corner accumulation. Using empirical scattering laws observed in previous experiments (scattering with a constant scattering angle), we next develop a two-dimension geometrical model and compute the phase space of trapped and periodic trajectories of swimmers inside a three-circles billiard. We find that the majority of cell trajectories end up in a corner, providing a geometrical mechanism for corner accumulation. Incorporating the distribution of scattering angles observed in our experiments and including hydrodynamic interactions between the cells and the surfaces into the geometrical model enables us to reproduce the experimental probability density function of micro-swimmers in microfluidic chambers. Both our experiments and models demonstrate therefore that motility leads generically to trapping in complex geometries.

Active particles with polar alignment in ring-shaped confinement

We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.

Simulations of structure formation by confined dipolar active particles

Dipolar active particles describe a class of self-propelled, biological or artificial particles equipped with an internal (typically magnetic) dipole moment. Because of the interplay between self-propulsion and dipole-dipole interactions, complex collective behavior is expected to emerge in systems of such particles. Here, we use Brownian dynamics simulations to explore this collective behavior. We focus on the structures that form in small systems in spatial confinement. We quantify the type of structures that emerge and how they depend on the self-propulsion speed and the dipolar (magnetic) strength of the particles. We observe that the dipolar active particles self-assemble into chains and rings. The dominant configuration is quantified with an order parameter for chain and ring formation and shown to depend on the self-propulsion speed and the dipolar magnetic strength of the particles. In addition, we show that the structural configurations are also affected by the confining walls. To that end, we compare different confining geometries and study the impact of a reorienting 'wall torque' upon collisions of a particle with a wall. Our results indicate that dipolar interactions can further enhance the already rich variety of collective behaviors of active particles.

Sorting and Extraction of Self-Propelled Chiral Particles by Polarized Wall Currents

The dynamics of self-propelled particles with curved trajectories is investigated. Two modes are observed, a bulk mode with a quasicircular motion and a surface mode with the particles following the walls. The surface mode is the only mode of ballistic transport and the particle current is polar and depends on the particles' chirality. We show that a robust sorting and extraction occurs when the particles explore a domain with two exit gates collecting selectively the particles circling left and right. With a counterslope, the extraction rate is found to increase while the sorting error is reduced.

Spatiotemporal dynamics of a self-propelled system with opposing alignment and repulsive forces

Effect of concurrent alignment and repulsion is studied in the purview of a confined active matter system using a modified force-based Vicsek model. On alteration of the alignment and the repulsive force parameters, a low alignment random phase, a midrange alignment milling phase, and a high alignment oscillatory phase are identified. Based on the particle aggregations, the milling phase is further classified into three subphases, two of which are spatial patterns: one consisting of compact ring-shaped mills and the other incorporating both rings and clusters. A correlation function based on the inner product of spatial velocity fluctuations of the particles shows a high correlation length for the ringed milling and the rings-clusters hybrid milling state. On analyzing temporal velocity fluctuations of particles through chaos detection techniques, low alignment and high alignment states are indicative of chaos, while the middle order alignment is symbolic of periodicity. The extent of synchronization of the particles' motion is analyzed through a Hilbert transform-based mean frequency approach, leading to the detection of a weak chimera state in the case of the spatial structures. The ringed milling state shows a unique category of weak chimera consisting of multiple oscillator groups showcasing different synchronization frequencies coexisting with desynchronized oscillators.

Trapping of swimming microalgae in foam

Massive foam formation in aquatic environments is a seasonal event that has a significant impact on the stability of marine ecosystems. Liquid foams are known to filter passive solid particles, with large particles remaining trapped by confinement in the network of liquid channels and small particles being freely advected by the gravity-driven flow. By contrast, the potential role of a similar retention effect on biologically active particles such as phytoplankton cells is still relatively unknown. To assess if phytoplankton cells are passively advected through a foam, the model unicellular motile alga Chlamydomonas reinhardtii (CR) was incorporated in a bio-compatible foam, and the number of cells escaping the foam at the bottom was measured in time. Comparing the escape dynamics of living and dead CR cells, we found that dead cells are totally advected by the liquid flow towards the bottom of the foam, as expected since the diameter of CR remains smaller than the typical foam channel diameter. By contrast, living motile CR cells escape the foam at a significantly lower rate: after 2 hours, up to 60% of the injected cells may remain blocked in the foam, while 95% of the initial liquid volume in the foam has been drained out of the foam. Microscopic observation of the swimming CR cells in a chamber mimicking the cross-section of foam internal channels revealed that swimming CR cells accumulate near channels corners. A theoretical analysis based on the probability density measurements in the micro chambers has shown that this trapping at the microscopic scale contributes to explain the macroscopic retention of the microswimmers in the foam. At the crossroads of distinct fields including marine ecology of planktonic organisms, fluid dynamics of active particles in a confined environment and the physics of foam, this work represents a significant step in the fundamental understanding of the ecological consequences of aquatic foams in water bodies.

Patterning non-equilibrium morphologies in stimuli-responsive gels through topographical confinement

Stimuli-responsive "smart" polymers have generated significant interest for introducing dynamic control into the properties of antifouling coatings, smart membranes, switchable adhesives and cell manipulation substrates. Switchable surface morphologies formed by confining stimuli-responsive gels to topographically structured substrates have shown potential for a variety of interfacial applications. Beyond patterning the equilibrium swelling behavior of gels, subjecting stimuli-responsive gels to topographical confinement could also introduce spatial gradients in the various timescales associated with gel deformation, giving rise to novel non-equilibrium morphologies. Here we show how by curing poly(N-isopropylacrylamide) (pNIPAAm)-based gel under confinement to a rigid, bumpy substrate, we can not only induce the surface curvature to invert with temperature, but also program the transient, non-equilibrium morphologies that emerge during the inversion process through changing the heating path. Finite element simulations show that the emergence of these transient morphologies is correlated with confinement-induced gradients in polymer concentration and position-dependent hydrostatic pressure within the gel. To illustrate the relevance of such morphologies in interfacial applications, we show how they enable us to control the gravity-induced assembly of colloidal particles and microalgae. Finally, we show how more complex arrangements in particle assembly can be created through controlling the thickness of the temperature-responsive gel over the bumps. Patterning stimuli-responsive gels on topographically-structured surfaces not only enables switching between two invertible topographies, but could also create opportunities for stimuli ramp-dependent control over the local curvature of the surface and emergence of unique transient morphologies. Harnessing these features could have potential in the design of multifunctional, actuatable materials for switchable adhesion, antifouling, cell manipulation, and liquid and particle transport surfaces.

Capillary Action in Scalar Active Matter

We study the capacity of active matter to rise in thin tubes against gravity and other related phenomena like wetting of vertical plates and spontaneous imbibition, where a wetting liquid is drawn into a porous medium. This capillary action or capillarity is well known in classical fluids and originates from attractive interactions between the liquid molecules and the container walls, and from the attraction of the liquid molecules among each other. We observe capillarity in a minimal model for scalar active matter with purely repulsive interactions, where an effective attraction emerges due to slowdown during collisions between active particles and between active particles and walls. Simulations indicate that the capillary rise in thin tubes is approximately proportional to the active sedimentation length λ and that the wetting height of a vertical plate grows superlinear with λ. In a disordered porous medium the imbibition height scales as ⟨h⟩∝λϕ_{m}, where ϕ_{m} is its packing fraction. These predictions are highly relevant for suspensions of sedimenting active colloids or motile bacteria in a porous medium under the influence of a constant force field.

Dynamic force measurements on swimming Chlamydomonas cells using micropipette force sensors

Flagella and cilia are cellular appendages that inherit essential functions of microbial life including sensing and navigating the environment. In order to propel a swimming microorganism they displace the surrounding fluid by means of periodic motions, while precisely timed modulations of their beating patterns enable the cell to steer towards or away from specific locations. Characterizing the dynamic forces, however, is challenging and typically relies on indirect experimental approaches. Here, we present direct in vivo measurements of the dynamic forces of motile Chlamydomonas reinhardtii cells in controlled environments. The experiments are based on partially aspirating a living microorganism at the tip of a micropipette force sensor and optically recording the micropipette's position fluctuations with high temporal and sub-pixel spatial resolution. Spectral signal analysis allows for isolating the cell-generated dynamic forces caused by the periodic motion of the flagella from background noise. We provide an analytic, elasto-hydrodynamic model for the micropipette force sensor and describe how to obtain the micropipette's full frequency response function from a dynamic force calibration. Using this approach, we measure the amplitude of the oscillatory forces during the swimming activity of individual Chlamydomonas reinhardtii cells of 26 ± 5 pN, resulting from the coordinated flagellar beating with a frequency of 49 ± 5 Hz. This dynamic micropipette force sensor technique generalizes the applicability of micropipettes as force sensors from static to dynamic force measurements, yielding a force sensitivity in the piconewton range. In addition to measurements in bulk liquid environment, we study the dynamic forces of the biflagellated microswimmer in the vicinity of a solid/liquid interface. As we gradually decrease the distance of the swimming microbe to the interface, we measure a significantly enhanced force transduction at distances larger than the maximum extent of the beating flagella, highlighting the importance of hydrodynamic interactions for scenarios in which flagellated microorganisms encounter surfaces.

Light Control of Localized Photobioconvection

Microorganismal motility is often characterized by complex responses to environmental physico-chemical stimuli. Although the biological basis of these responses is often not well understood, their exploitation already promises novel avenues to directly control the motion of living active matter at both the individual and collective level. Here we leverage the phototactic ability of the model microalga Chlamydomonas reinhardtii to precisely control the timing and position of localized cell photoaccumulation, leading to the controlled development of isolated bioconvective plumes. This novel form of photobioconvection allows a precise, fast, and reconfigurable control of the spatiotemporal dynamics of the instability and the ensuing global recirculation, which can be activated and stopped in real time. A simple continuum model accounts for the phototactic response of the suspension and demonstrates how the spatiotemporal dynamics of the illumination field can be used as a simple external switch to produce efficient bio mixing.

Ideal circle microswimmers in crowded media

Microswimmers are exposed in nature to crowded environments and their transport properties depend in a subtle way on the interaction with obstacles. Here, we investigate a model for a single ideal circle swimmer exploring a two-dimensional disordered array of impenetrable obstacles. The microswimmer moves on circular orbits in the freely accessible space and follows the surface of an obstacle for a certain time upon collision. Depending on the obstacle density and the radius of the circular orbits, the microswimmer displays either long-range transport or is localized in a finite region. We show that there are transitions from two localized states to a diffusive state each driven by an underlying static percolation transition. We determine the non-equilibrium state diagram and calculate the mean-square displacements and diffusivities by computer simulations. Close to the transition lines transport becomes subdiffusive which is rationalized as a dynamic critical phenomenon.

Maximum in density heterogeneities of active swimmers

Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae can exhibit spontaneous density heterogeneities at large enough concentrations. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and Péclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large Péclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.

Tailored environments to study motile cells and pathogens

Motile cells and pathogens migrate in complex environments and yet are mostly studied on simple 2D substrates. In order to mimic the diverse environments of motile cells, a set of assays including substrates of defined elasticity, microfluidics, micropatterns, organotypic cultures, and 3D gels have been developed. We briefly introduce these and then focus on the use of micropatterned pillar arrays, which help to bridge the gap between 2D and 3D. These structures are made from polydimethylsiloxane, a moldable plastic, and their use has revealed new insights into mechanoperception in Caenorhabditis elegans, gliding motility of Plasmodium, swimming of trypanosomes, and nuclear stability in cancer cells. These studies contributed to our understanding of how the environment influences the respective cell and inform on how the cells adapt to their natural surroundings on a cellular and molecular level.