Biological Microswimmers Research Articles

Electrotaxis of Self-Propelling Artificial Swimmers in Microchannels.

Biological microswimmers alter their swimming trajectories to follow the direction of an applied electric field, exhibiting electrotaxis. We show that synthetic active droplet microswimmers also autonomously change swimming trajectories in microchannels, even undergoing "U-turns," in response to an electric field, mimicking electrotaxis. We exploit such electrotaxis, in the presence of an external flow, to robustly tune the swimming trajectory of active droplets between wall-adjacent, oscillatory, and channel centerline swimming. A general hydrodynamic model demonstrates that the electrotactic dynamics is governed by the electrical effects due to the swimmer's inherent surface charge, besides its motility, hydrodynamic wall interactions, and relative orientations of the electric field and imposed flow. Our study demonstrates a simple method for controlling active agents in complex geometries for microrobotic applications, like autonomous cargo delivery.

Elastic interactions compete with persistent cell motility to drive durotaxis

Many animal cells that crawl on extracellular substrates exhibit durotaxis, i.e., directed migration toward stiffer substrate regions. This has implications in several biological processes including tissue development and tumor progression. Here, we introduce a phenomenological model for single-cell durotaxis that incorporates both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. Our model is motivated by a key observation in an early demonstration of durotaxis: a single, contractile cell at a sharp interface between a softer and a stiffer region of an elastic substrate reorients and migrates toward the stiffer region. We model migrating cells as self-propelling, persistently motile agents that exert contractile traction forces on their elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential. The dynamics is determined by two crucial parameters: the strength of the cellular traction-induced boundary elastic interaction (A), and the persistence of cell motility (Pe). Elastic forces and torques resulting from the potential orient cells perpendicular (parallel) to the boundary and accumulate (deplete) them at the clamped (free) boundary. Thus, a clamped boundary induces an attractive potential that drives durotaxis, while a free boundary induces a repulsive potential that prevents antidurotaxis. By quantifying the steady-state position and orientation probability densities, we show how the extent of accumulation (depletion) depends on the strength of the elastic potential and motility. We compare and contrast crawling cells with biological microswimmers and other synthetic active particles, where accumulation at confining boundaries is well known. We define metrics quantifying boundary accumulation and durotaxis, and present a phase diagram that identifies three possible regimes: durotaxis, and adurotaxis with and without motility-induced accumulation at the boundary. Overall, our model predicts how durotaxis depends on cell contractility and motility, successfully explains some previous observations, and provides testable predictions to guide future experiments.

Motility and pairwise interactions of chemically active droplets in one-dimensional confinement.

Self-propelled droplets serve as ideal model systems to delve deeper into understanding the motion of biological microswimmers by simulating their motility. Biological microorganisms are renowned for showcasing a diverse array of dynamic swimming behaviors when confronted with physical constraints. This study aims to elucidate the impact of physical constraints on swimming characteristics of biological microorganisms. To achieve this, we present observations on the individual and pairwise behavior of micellar solubilized self-propelled 4-cyano-4'-pentyl-biphenyl (5CB) oil droplets in a square capillary channel filled with a surfactant trimethyl ammonium bromide aqueous solution. To explore the effect of the underlying Péclet number of the swimming droplets, the study is also performed in the presence of additives such as high molecular weight polymer polyethylene oxide and molecular solute glycerol. The capillary confinement restricts droplet to predominantly one-dimensional motion, albeit with noticeable differences in their motion across the three scenarios. Through a characterization of the chemical and hydrodynamic flow fields surrounding the droplets, we illustrate that the modification of the droplets' chemical field due to confinement varies significantly based on the underlying differences in the Péclet number in these cases. This alteration in the chemical field distribution notably affects the individual droplets' motion. Moreover, these distinct chemical field interactions between the droplets also lead to variations in their pairwise motion, ranging from behaviors like chasing to scattering.

Chemotactic behavior for a self-phoretic Janus particle near a patch source of fuel.

Many biological microswimmers are capable of chemotaxis, i.e., they can sense an ambient chemical gradient and adjust their mechanism of motility to move towards or away from the source of the gradient. Synthetic active colloids endowed with chemotactic behavior hold considerable promise for targeted drug delivery and the realization of programmable and reconfigurable materials. Here, we study the chemotactic behavior of a Janus particle, which converts "fuel" molecules, released at an axisymmetric chemical patch located on a planar wall, into "product" molecules at its catalytic cap and moves by self-phoresis induced by the product. The chemotactic behavior is characterized as a function of the interplay between the rates of release (at the patch) and the consumption (at the particle) of fuel, as well as of details of the phoretic response of the particle (i.e., its phoretic mobility). Among other results, we find that, under certain conditions, the particle is attracted to a stable "hovering state" in which it aligns its axis normal to the wall and rests (positions itself) at an activity-dependent distance above the center of the patch.

Motion of microswimmers in cylindrical microchannels.

Biological and artificial microswimmers often have to propel through a variety of environments, ranging from heterogeneous suspending media to strong geometrical confinement. Under confinement, local flow fields generated by microswimmers, and steric and hydrodynamic interactions with their environment determine the locomotion. We propose a squirmer-like model to describe the motion of microswimmers in cylindrical microchannels, where propulsion is generated by a fixed surface slip velocity. The model is studied using an approximate analytical solution for cylindrical swimmer shapes, and by numerical hydrodynamics simulations for spherical and spheroidal shapes. For the numerical simulations, we employ the dissipative particle dynamics method for modelling fluid flow. Both the analytical model and simulations show that the propulsion force increases with increasing confinement. However, the swimming velocity under confinement remains lower than the swimmer speed without confinement for all investigated conditions. In simulations, different swimming modes (i.e. pusher, neutral, puller) are investigated, and found to play a significant role in the generation of propulsion force when a swimmer approaches a dead end of a capillary tube. Propulsion generation in confined systems is local, such that the generated flow field generally vanishes beyond the characteristic size of the swimmer. These results contribute to a better understanding of microswimmer force generation and propulsion under strong confinement, including the motion in porous media and in narrow channels.

Hydrodynamic pursuit by cognitive self-steering microswimmers

The properties of biological microswimmers are mostly determined by fluid-mediated interactions, which govern their propulsion, perception of their surrounding, and the steering of their motion for pursuit. Transferring similar functionalities to synthetic microswimmers poses major challenges, and the design of favorable steering and pursuit strategies is fundamental in such an endeavor. Here, we employ a squirmer model to investigate the pursuit of pursuer-target pairs with an implicit sensing mechanism and limited hydrodynamic steering abilities of the pursuer. Two hydrodynamic steering strategies are studied for the pursuer’s propulsion direction by adaptation of its surface flow field: reorientation toward the target with limited maneuverability, and alignment with the target’s propulsion direction combined with speed adaptation. Depending on the nature of the microswimmer propulsion (puller, pusher) and the velocity-adaptation scheme, stable cooperatively moving states can be achieved, where pursuer and target mutually affect their motion and trajectories.

Dynamics of squirmers in explicitly modeled polymeric fluids (a)

Biological microswimmers such as bacteria and sperm cells often encounter complex biological fluid environments. Here we use the well-known squirmer microswimmer model to show the importance of the local fluid microstructure and non-continuum effects on their swimming speed in different polymeric and filamentous fluids. Surprisingly, we find that different squirmer types move at considerably different speed in filamentous fluids which cannot be explained by existing continuum models, but by considering the local fluid and polymer properties around the squirmers. Furthermore, direct squirmer-polymer interactions slow down in particular pushers by trapping large stiff filaments in a self-generated recirculation region in front of them.

Learning to cooperate for low-Reynolds-number swimming: a model problem for gait coordination

Biological microswimmers can coordinate their motions to exploit their fluid environment—and each other—to achieve global advantages in their locomotory performance. These cooperative locomotion require delicate adjustments of both individual swimming gaits and spatial arrangements of the swimmers. Here we probe the emergence of such cooperative behaviors among artificial microswimmers endowed with artificial intelligence. We present the first use of a deep reinforcement learning approach to empower the cooperative locomotion of a pair of reconfigurable microswimmers. The AI-advised cooperative policy comprises two stages: an approach stage where the swimmers get in close proximity to fully exploit hydrodynamic interactions, followed a synchronization stage where the swimmers synchronize their locomotory gaits to maximize their overall net propulsion. The synchronized motions allow the swimmer pair to move together coherently with an enhanced locomotion performance unattainable by a single swimmer alone. Our work constitutes a first step toward uncovering intriguing cooperative behaviors of smart artificial microswimmers, demonstrating the vast potential of reinforcement learning towards intelligent autonomous manipulations of multiple microswimmers for their future biomedical and environmental applications.

Dynamics of Active SiO2-Pt Janus Colloids in Dilute Poly(ethylene oxide) Solutions.

Self-propelled Janus colloids (JCs) have recently gained much attention due to their ability to move autonomously and mimic biological microswimmers. This ability makes them suitable for prospective drug/cargo-delivery applications in microscopic domains. Understanding their dynamics in surroundings doped with macromolecules such as polymers is crucial, as most of the target application media are complex in nature. In this study, we investigate the self-diffusiophoretic motion of hydrogen peroxide-fuelled SiO2-Pt JCs in the presence of dilute amounts of poly(ethylene oxide) (PEO). Despite the addition of PEO chains producing a Newtonian behavior with negligible increase in viscosity, the ballistic movement and rotational fluctuations of active JCs are observed to be significantly suppressed. With an increase in the polymer concentration, this leads to a transition from smooth to jittery to cage-hopping to the arrested motion of active JCs. We further propose that the anisotropic interaction of the polymers with the JC increases the "local drag" of the medium, resulting in the unusual impediment of the active motion.

Island hopping of active colloids.

Individual self-propelled colloidal particles, like active Brownian particles (ABP) or run-and-tumble (RT) swimmers, exhibit characteristic and well-known motion patterns. However, their interaction with obstacles remains an open and important problem. We here investigate the two-dimensional motion of silica-gold Janus particles (JP) suspended in a bath of smaller silica passive particles. Actuated by AC electric fields, the JP cruise through passive colloids organized in 'islands' due to attractive electrohydrodynamic (EHD) flows. A typical island contains dozens of particles. The JP travels straight in obstacle-free regions and reorients abruptly upon collision with an island. As an underlying mechanism, we propose that the scattering events are caused by the interplay of EHD flows, self-propulsion and local torques. The combination of directed motion and sudden reorientations leads to active trajectories resembling the RT behavior of biological microswimmers.

Sync and Swarm: Solvable Model of Nonidentical Swarmalators.

We study a model of nonidentical swarmalators, generalizations of phase oscillators that both sync in time and swarm in space. The model produces four collective states: asynchrony, sync clusters, vortexlike phase waves, and a mixed state. These states occur in many real-world swarmalator systems such as biological microswimmers, chemical nanomotors, and groups of drones. A generalized Ott-Antonsen ansatz provides the first analytic description of these states and conditions for their existence. We show how this approach may be used in studies of active matter and related disciplines.

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

This articleprovides 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.

Oscillatory rheotaxis of artificial swimmers in microchannels

Biological microswimmers navigate upstream of an external flow with trajectories ranging from linear to spiralling and oscillatory. Such a rheotactic response primarily stems from the hydrodynamic interactions triggered by the complex shapes of the microswimmers, such as flagellar chirality. We show here that a self-propelling droplet exhibits oscillatory rheotaxis in a microchannel, despite its simple spherical geometry. Such behaviour has been previously unobserved in artificial swimmers. Comparing our experiments to a purely hydrodynamic theory model, we demonstrate that the oscillatory rheotaxis of the droplet is primarily governed by both the shear flow characteristics and the interaction of the finite-sized microswimmer with all four microchannel walls. The dynamics can be controlled by varying the external flow strength, even leading to the rheotactic trapping of the oscillating droplet. Our results provide a realistic understanding of the behaviour of active particles navigating in confined microflows relevant in many biotechnology applications.

Activity-induced interactions and cooperation of artificial microswimmers in one-dimensional environments

Cooperative motion in biological microswimmers is crucial for their survival as it facilitates adhesion to surfaces, formation of hierarchical colonies, efficient motion, and enhanced access to nutrients. Here, we confine synthetic, catalytic microswimmers along one-dimensional paths and demonstrate that they too show a variety of cooperative behaviours. We find that their speed increases with the number of swimmers, and that the activity induces a preferred distance between swimmers. Using a minimal model, we ascribe this behavior to an effective activity-induced potential that stems from a competition between chemical and hydrodynamic coupling. These interactions further induce active self-assembly into trains where swimmers move at a well-separated, stable distance with respect to each other, as well as compact chains that can elongate, break-up, become immobilized and remobilized. We identify the crucial role that environment morphology and swimmer directionality play on these highly dynamic chain behaviors. These activity-induced interactions open the door toward exploiting cooperation for increasing the efficiency of microswimmer motion, with temporal and spatial control, thereby enabling them to perform intricate tasks inside complex environments.

The effect of particle geometry on squirming through a shear-thinning fluid

Biological and artificial microswimmers often encounter fluid media with non-Newtonian rheological properties. In particular, many biological fluids such as blood and mucus are shear-thinning. Recent studies have demonstrated how shear-thinning rheology can impact substantially the propulsion performance in different manners. In this work, we examine the effect of geometrical shape upon locomotion in a shear-thinning fluid using a prolate spheroidal squirmer model. We use a combination of asymptotic analysis and numerical simulations to quantify how particle geometry impacts the speed and the energetic cost of swimming. The results demonstrate the advantages of spheroidal over spherical swimmers in terms of both swimming speed and energetic efficiency when squirming through a shear-thinning fluid. More generally, the findings suggest the possibility of tuning the swimmer geometry to better exploit non-Newtonian rheological behaviours for more effective locomotion in complex fluids.

Upstream Rheotaxis of Catalytic Janus Spheres.

Fluid flow is ubiquitous in many environments that form habitats for microorganisms. Therefore, it is not surprising that both biological and artificial microswimmers show responses to flows that are determined by the interplay of chemical and physical factors. In particular, to deepen the understanding of how different systems respond to flows, it is crucial to comprehend the influence played by swimming pattern. The tendency of organisms to navigate up or down the flow is termed rheotaxis. Early theoretical studies predicted a positive rheotactic response for puller-type spherical Janus micromotors. However, recent experimental studies have focused on pusher-type Janus particles, finding that they exhibit cross-stream migration in externally applied flows. To study the response to the flow of swimmers with a qualitatively different flow pattern, we introduce Cu@SiO2 micromotors that swim toward their catalytic cap. On the basis of experimental observations, and supported by flow field calculations using a model for self-electrophoresis, we hypothesize that they behave effectively as a puller-type system. We investigate the effect of externally imposed flow on these spherically symmetrical Cu@SiO2 active Janus colloids, and we indeed observe a steady upstream directional response. Through a simple squirmer model for a puller, we recover the major experimental observations. Additionally, the model predicts a "jumping" behavior for puller-type micromotors at high flow speeds. Performing additional experiments at high flow speeds, we capture this phenomenon, in which the particles "roll" with their swimming axes aligned to the shear plane, in addition to being dragged downstream by the fluid flow.

Anisotropic diffusion of ellipsoidal tracers in microswimmer suspensions

Tracer particles immersed in suspensions of biological microswimmers such as E. coli or C. reinhardtii display phenomena unseen in conventional equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value and non-Gaussian displacement statistics. In dilute, 3-dimensional suspensions, these phenomena have typically been explained by the hydrodynamic advection of point tracers by isolated microswimmers, while, at higher concentrations, correlations between pusher microswimmers such as E. coli can increase the effective diffusivity even further. Anisotropic tracers in active suspensions can be expected to exhibit even more complex behaviour than spherical ones, due to the presence of a nontrivial translation-rotation coupling. Using large-scale lattice Boltzmann simulations of model microswimmers described by extended force dipoles, we study the motion of ellipsoidal point tracers immersed in 3-dimensional microswimmer suspensions. We find that the rotational diffusivity of tracers is much less affected by swimmer-swimmer correlations than the translational diffusivity. We furthermore study the anisotropic translational diffusion in the particle frame and find that, in pusher suspensions, the diffusivity along the ellipsoid major axis is higher than in the direction perpendicular to it, albeit with a smaller ratio than for Brownian diffusion. Thus, we find that far field hydrodynamics cannot account for the anomalous coupling between translation and rotation observed in experiments, as was recently proposed. Finally, we study the probability distributions (PDFs) of translational and rotational displacements. In accordance with experimental observations, for short observation times we observe strongly non-Gaussian PDFs that collapse when rescaled with their variance, which we attribute to the ballistic nature of tracer motion at short times.

Microswimming in viscoelastic fluids

The locomotion of microorganisms and spermatozoa in complex viscoelastic fluids is of critical importance in many biological processes such as fertilization, infection, and biofilm formation. Depending on their propulsion mechanisms, microswimmers display various responses to a complex fluid environment: increasing or decreasing their swimming speed and efficiency, modifying their propulsion kinematics and swimming gaits, and experiencing different hydrodynamic interactions with their surroundings. In this article, we review the fundamental physics of locomotion of biological and synthetic microswimmers in complex viscoelastic fluids. Starting from a continuum framework, we describe the main theoretical approaches developed to model microswimming in viscoelastic fluids, which typically rely on asymptotically-small dimensionless parameters. We then summarize recent progress on the mobility of single cells propelled by cilia, waving flagella and rotating helical flagella in unbounded viscoelastic fluids. We next briefly discuss the impact of other physical factors, including the micro-scale heterogeneity of complex biological fluids, the role of Brownian fluctuations of the microswimmers, the effect of polymer entanglement and the influence of shear-thinning viscosity. In particular, for solution of long polymer chains whose sizes are comparable to the radius of flagella, continuum models cannot be used and instead Brownian Dynamics for the polymers can predict the swimming dynamics. Finally, we discuss the effect of viscoelasticity on the dynamics of microswimmers in the presence of surfaces or external flows and its impact on collective cellular behavior.

Optimal ciliary locomotion of axisymmetric microswimmers

Many biological microswimmers locomote by periodically beating the densely packed cilia on their cell surface in a wave-like fashion. While the swimming mechanisms of ciliated microswimmers have been extensively studied both from the analytical and the numerical point of view, optimisation of the ciliary motion of microswimmers has received limited attention, especially for non-spherical shapes. In this paper, using an envelope model for the microswimmer, we numerically optimise the ciliary motion of a ciliate with an arbitrary axisymmetric shape. Forward solutions are found using a fast boundary-integral method, and the efficiency sensitivities are derived using an adjoint-based method. Our results show that a prolate microswimmer with a $2\,{:}\,1$ aspect ratio shares similar optimal ciliary motion as the spherical microswimmer, yet the swimming efficiency can increase two-fold. More interestingly, the optimal ciliary motion of a concave microswimmer can be qualitatively different from that of the spherical microswimmer, and adding a constraint to the cilia length is found to improve, on average, the efficiency for such swimmers.

Reconfigurable artificial microswimmers with internal feedback

Self-propelling microparticles are often proposed as synthetic models for biological microswimmers, yet they lack the internally regulated adaptation of their biological counterparts. Conversely, adaptation can be encoded in larger-scale soft-robotic devices but remains elusive to transfer to the colloidal scale. Here, we create responsive microswimmers, powered by electro-hydrodynamic flows, which can adapt their motility via internal reconfiguration. Using sequential capillary assembly, we fabricate deterministic colloidal clusters comprising soft thermo-responsive microgels and light-absorbing particles. Light absorption induces preferential local heating and triggers the volume phase transition of the microgels, leading to an adaptation of the clusters’ motility, which is orthogonal to their propulsion scheme. We rationalize this response via the coupling between self-propulsion and variations of particle shape and dielectric properties upon heating. Harnessing such coupling allows for strategies to achieve local dynamical control with simple illumination patterns, revealing exciting opportunities for developing tactic active materials.