Chlamydomonas swims with two "gears" in a eukaryotic version of run-and-tumble locomotion

The younger flagellum sets the beat for Chlamydomonas reinhardtii

Eukaryotes swim with coordinated flagellar (ciliary) beating and steer by fine-tuning the coordination. The model organism for studying flagellate motility, Chlamydomonas reinhardtii, employs synchronous, breaststroke-like flagellar beating to swim, and it modulates the beating amplitudes differentially to steer. This strategy hinges on both inherent flagellar asymmetries (e.g. different response to chemical messengers) and such asymmetries being effectively coordinated in the synchronous beating. In C. reinhardtii, the synchrony of beating is known to be supported by a mechanical connection between flagella; however, how flagellar asymmetries persist in the synchrony remains elusive. For example, it has been speculated for decades that one flagellum leads the beating, as its dynamic properties (i.e. frequency, waveform, etc.) appear to be copied by the other one. In this study, we combine experiments, computations, and modeling efforts to elucidate the roles played by each flagellum in synchronous beating. With a non-invasive technique to selectively load each flagellum, we show that the coordinated beating essentially only responds to load exerted on the cis flagellum; and that such asymmetry in response derives from a unilateral coupling between the two flagella. Our results highlight a distinct role for each flagellum in coordination and have implication for biflagellates' tactic behaviors.

Hydrodynamic synchronization of elastic cilia: How surface effects determine the characteristics of metachronal waves

Cilia are hairlike microactuators whose cyclic motion is specialized to propel extracellular fluids at low Reynolds numbers. Clusters of these organelles can form synchronized beating patterns, called metachronal waves, which presumably arise from hydrodynamic interactions. We model hydrodynamically interacting cilia by microspheres elastically bound to circular orbits, whose inclinations with respect to a no-slip wall model the ciliary power and recovery stroke, resulting in an anisotropy of the viscous flow. We derive a coupled phase-oscillator description by reducing the microsphere dynamics to the slow timescale of synchronization and determine analytical metachronal wave solutions and their stability in a periodic chain setting. In this framework, a simple intuition for the hydrodynamic coupling between phase oscillators is established by relating the geometry of flow near the surface of a cell or tissue to the directionality of the hydrodynamic coupling functions. This intuition naturally explains the properties of the linear stability of metachronal waves. The flow near the surface stabilizes metachronal waves with long wavelengths propagating in the direction of the power stroke and, moreover, metachronal waves with short wavelengths propagating perpendicularly to the power stroke. Performing simulations of phase-oscillator chains with periodic boundary conditions, we indeed find that both wave types emerge with a variety of linearly stable wave numbers. In open chains of phase oscillators, the dynamics of metachronal waves is fundamentally different. Here the elasticity of the model cilia controls the wave direction and selects a particular wave number: At large elasticity, waves traveling in the direction of the power stroke are stable, whereas at smaller elasticity waves in the opposite direction are stable. For intermediate elasticity both wave directions coexist. In this regime, waves propagating towards both ends of the chain form, but only one wave direction prevails, depending on the elasticity and initial conditions.

Bioelectric control of locomotor gaits in the walking ciliate Euplotes

Diverse animal species exhibit highly stereotyped behavioral actions and locomotor sequences as they explore their natural environments. In many such cases, the neural basis of behavior is well established, where dedicated neural circuitry contributes to the initiation and regulation of certain response sequences. At the microscopic scale, single-celled eukaryotes (protists) also exhibit remarkably complex behaviors and yet are completely devoid of nervous systems. Here, to address the question of how single cells control behavior, we study locomotor patterning in the exemplary hypotrich ciliate Euplotes, a highly polarized cell, which actuates a large number of leg-like appendages called cirri (each a bundle of ∼25-50 cilia) to swim in fluids or walk on surfaces. As it navigates its surroundings, a walking Euplotes cell is routinely observed to perform side-stepping reactions, one of the most sophisticated maneuvers ever observed in a single-celled organism. These are spontaneous and stereotyped reorientation events involving a transient and fast backward motion followed by a turn. Combining high-speed imaging with simultaneous time-resolved electrophysiological recordings, we show that this complex coordinated motion sequence is tightly regulated by rapid membrane depolarization events, which orchestrate the activity of different cirri on the cell. Using machine learning and computer vision methods, we map detailed measurements of cirri dynamics to the cell's membrane bioelectrical activity, revealing a differential response in the front and back cirri. We integrate these measurements with a minimal model to understand how Euplotes-a unicellular organism-manipulates its membrane potential to achieve real-time control over its motor apparatus.

AI-aided geometric design of anti-infection catheters

Bacteria can swim upstream in a narrow tube and pose a clinical threat of urinary tract infection to patients implanted with catheters. Coatings and structured surfaces have been proposed to repel bacteria, but no such approach thoroughly addresses the contamination problem in catheters. Here, on the basis of the physical mechanism of upstream swimming, we propose a novel geometric design, optimized by an artificial intelligence model. Using Escherichia coli, we demonstrate the anti-infection mechanism in microfluidic experiments and evaluate the effectiveness of the design in three-dimensionally printed prototype catheters under clinical flow rates. Our catheter design shows that one to two orders of magnitude improved suppression of bacterial contamination at the upstream end, potentially prolonging the in-dwelling time for catheter use and reducing the overall risk of catheter-associated urinary tract infection.

Biohybrid Microalgae Robots: Design, Fabrication, Materials, and Applications

The integration of microorganisms and engineered artificial components has shown considerable promise for creating biohybrid microrobots. The unique features of microalgae make them attractive candidates as natural actuation materials for the design of biohybrid microrobotic systems. In this review, microalgae-based biohybrid microrobots are introduced for diverse biomedical and environmental applications. The distinct propulsion and phototaxis behaviors of green microalgae, as well as important properties from other photosynthetic microalga systems (blue-green algae and diatom) that are crucial to constructing powerful biohybrid microrobots, will be described first. Then the focus is on chemical and physical routes for functionalizing the algae surface with diverse reactive materials toward the fabrication of advanced biohybrid microalgae robots. Finally, representative applications of such algae-driven microrobots are presented, including drug delivery, imaging, and water decontamination, highlighting the distinct advantages of these active biohybrid robots, along with future prospects and challenges.

Quantitative characterization of run-and-tumble statistics in bulk bacterial suspensions

We introduce a numerical method to extract the parameters of run-and-tumble dynamics from experimental measurements of the intermediate scattering function. We show that proceeding in Laplace space is unpractical and employ instead renewal processes to work directly in real time. We first validate our approach against data produced using agent-based simulations. This allows us to identify the length and time scales required for an accurate measurement of the motility parameters, including tumbling frequency and swim speed. We compare different models for the run-and-tumble dynamics by accounting for speed variability at the single-cell and population level, respectively. Finally, we apply our approach to experimental data on wild-type Escherichia coli obtained using differential dynamic microscopy.

Perspectives on Principles of Cellular Behavior from the Biophysics of Protists

Cells are the fundamental unit of biological organization. Although it may be easy to think of them as little more than the simple building blocks of complex organisms such as animals, single cells are capable of behaviors of remarkable apparent sophistication. This is abundantly clear when considering the diversity of form and function among the microbial eukaryotes, the protists. How might we navigate this diversity in the search for general principles of cellular behavior? Here, we review cases in which the intensive study of protists from the perspective of cellular biophysics has driven insight into broad biological questions of morphogenesis, navigation and motility, and decision making. We argue that applying such approaches to questions of evolutionary cell biology presents rich, emerging opportunities. Integrating and expanding biophysical studies across protist diversity, exploiting the unique characteristics of each organism, will enrich our understanding of general underlying principles.

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.

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.

Fast detection of slender bodies in high density microscopy data

Computer-aided analysis of biological microscopy data has seen a massive improvement with the utilization of general-purpose deep learning techniques. Yet, in microscopy studies of multi-organism systems, the problem of collision and overlap remains challenging. This is particularly true for systems composed of slender bodies such as swimming nematodes, swimming spermatozoa, or the beating of eukaryotic or prokaryotic flagella. Here, we develop a end-to-end deep learning approach to extract precise shape trajectories of generally motile and overlapping slender bodies. Our method works in low resolution settings where feature keypoints are hard to define and detect. Detection is fast and we demonstrate the ability to track thousands of overlapping organisms simultaneously. While our approach is agnostic to area of application, we present it in the setting of and exemplify its usability on dense experiments of swimming Caenorhabditis elegans. The model training is achieved purely on synthetic data, utilizing a physics-based model for nematode motility, and we demonstrate the model's ability to generalize from simulations to experimental videos.

A physics-based model of swarming jellyfish

We propose a model for the structure formation of jellyfish swimming based on active Brownian particles. We address the phenomena of counter-current swimming, avoidance of turbulent flow regions and foraging. We motivate corresponding mechanisms from observations of jellyfish swarming reported in the literature and incorporate them into the generic modelling framework. The model characteristics is tested in three paradigmatic flow environments.

Cells collectively migrate during ammonium chemotaxis in Chlamydomonas reinhardtii

The mechanisms governing chemotaxis in Chlamydomonas reinhardtii are largely unknown compared to those regulating phototaxis despite equal importance on the migratory response in the ciliated microalga. To study chemotaxis, we made a simple modification to a conventional Petri dish assay. Using the assay, a novel mechanism governing Chlamydomonas ammonium chemotaxis was revealed. First, we found that light exposure enhances the chemotactic response of wild-type Chlamydomonas strains, yet phototaxis-incompetent mutant strains, eye3-2 and ptx1, exhibit normal chemotaxis. This suggests that Chlamydomonas transduces the light signal pathway in chemotaxis differently from that in phototaxis. Second, we found that Chlamydomonas collectively migrate during chemotaxis but not phototaxis. Collective migration during chemotaxis is not clearly observed when the assay is conducted in the dark. Third, the Chlamydomonas strain CC-124 carrying agg1^-, the AGGREGATE1 gene (AGG1) null mutation, exhibited a more robust collective migratory response than strains carrying the wild-type AGG1 gene. The expression of a recombinant AGG1 protein in the CC-124 strain suppressed this collective migration during chemotaxis. Altogether, these findings suggest a unique mechanism; ammonium chemotaxis in Chlamydomonas is mainly driven by collective cell migration. Furthermore, it is proposed that collective migration is enhanced by light and suppressed by the AGG1 protein.

Translocator protein in the rise and fall of central nervous system neurons

Translocator protein (TSPO), a 18 kDa protein found in the outer mitochondrial membrane, has historically been associated with the transport of cholesterol in highly steroidogenic tissues though it is found in all cells throughout the mammalian body. TSPO has also been associated with molecular transport, oxidative stress, apoptosis, and energy metabolism. TSPO levels are typically low in the central nervous system (CNS), but a significant upregulation is observed in activated microglia during neuroinflammation. However, there are also a few specific regions that have been reported to have higher TSPO levels than the rest of the brain under normal conditions. These include the dentate gyrus of the hippocampus, the olfactory bulb, the subventricular zone, the choroid plexus, and the cerebellum. These areas are also all associated with adult neurogenesis, yet there is no explanation of TSPO's function in these cells. Current studies have investigated the role of TSPO in microglia during neuron degeneration, but TSPO's role in the rest of the neuron lifecycle remains to be elucidated. This review aims to discuss the known functions of TSPO and its potential role in the lifecycle of neurons within the CNS.

Dynamics and interactions of Quincke roller clusters: From orbits and flips to excited states

Active matter systems may be characterized by the conversion of energy into active motion, e.g., the self-propulsion of microorganisms. Artificial active colloids form models that exhibit essential properties of more complex biological systems but are amenable to laboratory experiments. While most experimental models consist of spheres, active particles of different shapes are less understood. Furthermore, interactions between these anisotropic active colloids are even less explored. Here, we investigate the motion of active colloidal clusters and the interactions between them. We focus on self-assembled dumbbells and trimers powered by an external dc electric field. For dumbbells, we observe an activity-dependent behavior of spinning, circular, and orbital motions. Moreover, collisions between dumbbells lead to the hierarchical self-assembly of tetramers and hexamers, both of which form rotational excited states. On the other hand, trimers exhibit flipping motion that leads to trajectories reminiscent of a honeycomb lattice.

Hydrodynamic clustering of two finite-length flagellated swimmers in viscoelastic fluids

Clustering of flagellated microswimmers such as sperm is often mediated by hydrodynamic interactions between them. To better understand the interaction of microswimmers in viscoelastic fluids, we perform two-dimensional simulations of two swimming sheets, using a viscoelastic version of the smoothed dissipative particle dynamics method that implements the Oldroyd-B fluid model. Elasticity of sheets (stiff versus soft) defines two qualitatively different regimes of clustering, where stiff sheets exhibit a much more robust clustering than soft sheets. A formed doublet of soft sheets generally swims faster than a single swimmer, while a pair of two stiff sheets normally shows no speed enhancement after clustering. A pair of two identical swimmers is stable for most conditions, while differences in the beating amplitudes and/or frequencies between the two sheets can destroy the doublet stability. Clustering of two distinct swimmers is most stable at Deborah numbers of De = τω ≈ 1 (τ is the relaxation time of a viscoelastic fluid and ω is the beating frequency), in agreement with experimental observations. Therefore, the clustering of two swimmers depends non-monotonically on De. Our results suggest that the cluster stability is likely a dominant factor which determines the cluster size of collectively moving flagellated swimmers.

Novel analytical tools reveal that local synchronization of cilia coincides with tissue-scale metachronal waves in zebrafish multiciliated epithelia

Motile cilia are hair-like cell extensions that beat periodically to generate fluid flow along various epithelial tissues within the body. In dense multiciliated carpets, cilia were shown to exhibit a remarkable coordination of their beat in the form of traveling metachronal waves, a phenomenon which supposedly enhances fluid transport. Yet, how cilia coordinate their regular beat in multiciliated epithelia to move fluids remains insufficiently understood, particularly due to lack of rigorous quantification. We combine experiments, novel analysis tools, and theory to address this knowledge gap. To investigate collective dynamics of cilia, we studied zebrafish multiciliated epithelia in the nose and the brain. We focused mainly on the zebrafish nose, due to its conserved properties with other ciliated tissues and its superior accessibility for non-invasive imaging. We revealed that cilia are synchronized only locally and that the size of local synchronization domains increases with the viscosity of the surrounding medium. Even though synchronization is local only, we observed global patterns of traveling metachronal waves across the zebrafish multiciliated epithelium. Intriguingly, these global wave direction patterns are conserved across individual fish, but different for left and right noses, unveiling a chiral asymmetry of metachronal coordination. To understand the implications of synchronization for fluid pumping, we used a computational model of a regular array of cilia. We found that local metachronal synchronization prevents steric collisions, i.e., cilia colliding with each other, and improves fluid pumping in dense cilia carpets, but hardly affects the direction of fluid flow. In conclusion, we show that local synchronization together with tissue-scale cilia alignment coincide and generate metachronal wave patterns in multiciliated epithelia, which enhance their physiological function of fluid pumping.

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.

Phototaxis of Chlamydomonas arises from a tuned adaptive photoresponse shared with multicellular Volvocine green algae

A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse of micropipette-held Chlamydomonas with 3D tracking of freely swimming cells, we show that such tuning also underlies its phototaxis. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of timescales between the flagellar photoresponse and phototurning, we develop an equation of motion that accurately describes the observed photoalignment. In showing that the adaptive timescales in Volvocine algae are tuned to the organisms' rotational periods across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium, and the flagellated hemispheres of Volvox.

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.

A one-dimensional three-state run-and-tumble model with a 'cell cycle'

We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferating mobile phases and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for the number density of settled cells. The latter displays a surprising super-ballistic scaling [Formula: see text] at early times. Including repulsive and attractive interactions between the mobile cell populations and the settled cells, we explore the stability of the system and employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.

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.

The role of disorder in the motion of chiral active particles in the presence of obstacles

The presence of obstacles is intuitively expected to hinder the diffusive transport of active particles. However, for chiral active particles, a low density of obstacles near a surface can enhance their diffusive behavior. Here, we study numerically the role that disorder plays in determining the transport dynamics of chiral active particles on surfaces with obstacles. We consider different densities of regularly spaced obstacles and distinct types of disorder: noise in the dynamics of the particle, quenched noise in the positions of the obstacles as well as obstacle size polydispersity. We show that, depending on the type and strength of the disorder, the presence of obstacles can either enhance or hinder transport, and discuss implications for the control of active transport in disordered media.

Dispersing swimming microalgae in self-assembled nanocellulose suspension: Unveiling living colloid dynamics in cholesteric liquid crystals

Active matter comprises individual energy-consuming components that convert locally stored energy into mechanical motion. Among these, liquid crystal dispersed self-propelled colloids have displayed fascinating dynamic effects and nonequilibrium behaviors. In this work, we introduce a new type of active soft matter based on swimming microalgae and lyotropic nanocellulose liquid crystal. Cellulose is a kind of biocompatible polysaccharide that nontoxic to living biological colloids. In contrast to microalgae locomotion in isotropic and low viscosity media, we demonstrate that the propulsion force of swimming microalgae can overcome the stabilizing elastic force in cholesteric nanocellulose liquid crystal, with the displacement dynamics (gait, direction, frequency, and speed) be altered by the surrounding medium. Simultaneously, the active stress and shear flow exerted by swimming microalgae can introduce local perturbation in surrounding liquid crystal orientation order. The latter effect yields hydrodynamic fluctuations in bulk phase as well as layer undulations, helicoidal axis splay deformation and director bending in the cholesteric assembly, which finally followed by a recovery according to the inherent viscoelasticity of liquid crystal matrix. Our results point to an unorthodox design concept to generate a new type of hybrid soft matter that combines nontoxic cholesteric liquid crystal and active particles, which are expected to open opportunities in biosensing and biomechanical applications.

Heterogeneous run-and-tumble motion accounts for transient non-Gaussian super-diffusion in haematopoietic multi-potent progenitor cells

Multi-potent progenitor (MPP) cells act as a key intermediary step between haematopoietic stem cells and the entirety of the mature blood cell system. Their eventual fate determination is thought to be achieved through migration in and out of spatially distinct niches. Here we first analyze statistically MPP cell trajectory data obtained from a series of long time-course 3D in vivo imaging experiments on irradiated mouse calvaria, and report that MPPs display transient super-diffusion with apparent non-Gaussian displacement distributions. Second, we explain these experimental findings using a run-and-tumble model of cell motion which incorporates the observed dynamical heterogeneity of the MPPs. Third, we use our model to extrapolate the dynamics to time-periods currently inaccessible experimentally, which enables us to quantitatively estimate the time and length scales at which super-diffusion transitions to Fickian diffusion. Our work sheds light on the potential importance of motility in early haematopoietic progenitor function.

A unicellular walker controlled by a microtubule-based finite-state machine

Cells are complex biochemical systems whose behaviors emerge from interactions among myriad molecular components. Computation is often invoked as a general framework for navigating this cellular complexity. However, it is unclear how cells might embody computational processes such that the theories of computation, including finite-state machine models, could be productively applied. Here, we demonstrate finite-state-machine-like processing embodied in cells using the walking behavior of Euplotes eurystomus, a ciliate that walks across surfaces using fourteen motile appendages (cirri). We found that cellular walking entails regulated transitions among a discrete set of gait states. The set of observed transitions decomposes into a small group of high-probability, temporally irreversible transitions and a large group of low-probability, time-symmetric transitions, thus revealing stereotypy in the sequential patterns of state transitions. Simulations and experiments suggest that the sequential logic of the gait is functionally important. Taken together, these findings implicate a finite-state-machine-like process. Cirri are connected by microtubule bundles (fibers), and we found that the dynamics of cirri involved in different state transitions are associated with the structure of the fiber system. Perturbative experiments revealed that the fibers mediate gait coordination, suggesting a mechanical basis of gait control.

Controlling dynamics in extended molecular frameworks

Molecular machines are essential dynamic components for fuel production, cargo delivery, information storage and processing in living systems. Scientists have demonstrated that they can design and synthesize artificial molecular machines that operate efficiently in isolation - for example, at high dilution in solution - fuelled by chemicals, electricity or light. To organize the spatial arrangement and motion of these machines within close proximity to one another in solid frameworks, such that useful macroscopic work can be performed, remains a challenge in both chemical and materials science. In this Review, we summarize the progress that has been made during the past decade in organizing dynamic molecular entities in such solid frameworks. Emerging applications of these dynamic smart materials in the contexts of molecular recognition, optoelectronics, drug delivery, photodynamic therapy and water desalination are highlighted. Finally, we review recent work on a new non-equilibrium adsorption phenomenon for which we have coined the term mechanisorption. The ability to use external energy to drive directional processes in mechanized extended frameworks augurs well for the future development of artificial molecular factories.

Recent Process in Microrobots: From Propulsion to Swarming for Biomedical Applications

Recently, robots have assisted and contributed to the biomedical field. Scaling down the size of robots to micro/nanoscale can increase the accuracy of targeted medications and decrease the danger of invasive operations in human surgery. Inspired by the motion pattern and collective behaviors of the tiny biological motors in nature, various kinds of sophisticated and programmable microrobots are fabricated with the ability for cargo delivery, bio-imaging, precise operation, etc. In this review, four types of propulsion-magnetically, acoustically, chemically/optically and hybrid driven-and their corresponding features have been outlined and categorized. In particular, the locomotion of these micro/nanorobots, as well as the requirement of biocompatibility, transportation efficiency, and controllable motion for applications in the complex human body environment should be considered. We discuss applications of different propulsion mechanisms in the biomedical field, list their individual benefits, and suggest their potential growth paths.

Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence

We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.

The dopamine circuit as a reward-taxis navigation system

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.

Nonlinear Phototaxis and Instabilities in Suspensions of Light-Seeking Algae

The mechanism by which living organisms seek optimal light conditions-phototaxis-is a fundamental process for motile photosynthetic microbes. It is involved in a broad array of natural processes and applications from bloom formation to the production of high-value chemicals in photobioreactors. Here, we show that a population of the model alga Chlamydomonas reinhardtii exhibits a highly sensitive nonlinear response to light and demonstrate that the self-organization of cells in a heterogeneous environment becomes unstable as the result of a coupling between bioconvective flows and phototaxis.

Coordination of two opposite flagella allows high-speed swimming and active turning of individual zoospores

Phytophthora species cause diseases in a large variety of plants and represent a serious agricultural threat, leading, every year, to multibillion dollar losses. Infection occurs when their biflagellated zoospores move across the soil at their characteristic high speed and reach the roots of a host plant. Despite the relevance of zoospore spreading in the epidemics of plant diseases, individual swimming of zoospores have not been fully investigated. It remains unknown about the characteristics of two opposite beating flagella during translation and turning, and the roles of each flagellum on zoospore swimming. Here, combining experiments and modeling, we show how these two flagella contribute to generate thrust when beating together, and identify the mastigonemes-attached anterior flagellum as the main source of thrust. Furthermore, we find that turning involves a complex active process, in which the posterior flagellum temporarily stops, while the anterior flagellum keeps on beating and changes its gait from sinusoidal waves to power and recovery strokes, similar to Chlamydomonas's breaststroke, to reorient its body to a new direction. Our study is a fundamental step toward a better understanding of the spreading of plant pathogens' motile forms, and shows that the motility pattern of these biflagellated zoospores represents a distinct eukaryotic version of the celebrated 'run-and-tumble' motility class exhibited by peritrichous bacteria.

Memory effects in spiral diffusion of rotary self-propellers

The coupling of deterministic rotary motion and stochastic orientational diffusion of a self-propeller leads to a spiral trajectory of the expected displacement. We extend our former analysis of spiral diffusion [Phys. Rev. E 94, 030601(R) (2016)10.1103/PhysRevE.94.030601] in the white-noise limit to a more realistic scenario of stochastic noise with Gaussian memory and orientational fluctuations driven by an Ornstein-Uhlenbeck process. A variety of dynamical regimes including crossovers from ballistic to diffusive to ballistic in the angular dynamics are determined by the inertial timescale, orientational diffusivity, and angular speed.

Synchronization in cilia carpets and the Kuramoto model with local coupling: Breakup of global synchronization in the presence of noise

Carpets of beating cilia represent a paradigmatic example of self-organized synchronization of noisy biological oscillators, characterized by traveling waves of cilia phase. We present a multi-scale model of a cilia carpet that comprises realistic hydrodynamic interactions between cilia computed for a chiral cilia beat pattern from unicellular Paramecium and active noise of the cilia beat. We demonstrate an abrupt loss of global synchronization beyond a characteristic noise strength. We characterize stochastic transitions between synchronized and disordered dynamics, which generalize the notion of phase slips in pairs of coupled noisy phase oscillators. Our theoretical work establishes a link between the two-dimensional Kuramoto model of phase oscillators with mirror-symmetric oscillator coupling and detailed models of biological oscillators with asymmetric, chiral interactions.

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.

A geometric criterion for the optimal spreading of active polymers in porous media

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with experiments of Escherichia coli, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. Our findings show that the spreading of active agents in porous media can be optimized by tuning their run lengths, which we rationalize using a coarse-grained model. More significantly, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. Our criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings.

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.

Estimating Entropy Production from Waiting Time Distributions

Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication, or locomotion. Given time series observations of intra-, inter-, or multicellular processes, a key challenge is to detect nonequilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice, as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and, hence, can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics, and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs, and mice.

Structural organization of the C1b projection within the ciliary central apparatus

Motile cilia have a '9+2' structure containing nine doublet microtubules and a central apparatus (CA) composed of two singlet microtubules with associated projections. The CA plays crucial roles in regulating ciliary motility. Defects in CA assembly or function usually result in motility-impaired or paralyzed cilia, which in humans causes disease. Despite their importance, the protein composition and functions of most CA projections remain largely unknown. Here, we combined genetic, proteomic and cryo-electron tomographic approaches to compare the CA of wild-type Chlamydomonas reinhardtii with those of three CA mutants. Our results show that two proteins, FAP42 and FAP246, are localized to the L-shaped C1b projection of the CA, where they interact with the candidate CA protein FAP413. FAP42 is a large protein that forms the peripheral 'beam' of the C1b projection, and the FAP246-FAP413 subcomplex serves as the 'bracket' between the beam (FAP42) and the C1b 'pillar' that attaches the projection to the C1 microtubule. The FAP246-FAP413-FAP42 complex is essential for stable assembly of the C1b, C1f and C2b projections, and loss of these proteins leads to ciliary motility defects.

The 3D architecture and molecular foundations of de novo centriole assembly via bicentrioles

Centrioles are structurally conserved organelles, composing both centrosomes and cilia. In animal cycling cells, centrioles often form through a highly characterized process termed canonical duplication. However, a large diversity of eukaryotes assemble centrioles de novo through uncharacterized pathways. This unexplored diversity is key to understanding centriole assembly mechanisms and how they evolved to assist specific cellular functions. Here, we show that, during spermatogenesis of the bryophyte Physcomitrium patens, centrioles are born as a co-axially oriented centriole pair united by a cartwheel. Interestingly, we observe that these centrioles are twisted in opposite orientations. Microtubules emanate from the bicentrioles, which localize to the spindle poles during cell division. After their separation, the two resulting sister centrioles mature asymmetrically, elongating specific microtubule triplets and a naked cartwheel. Subsequently, two motile cilia are assembled that appear to alternate between different motility patterns. We further show that centriolar components SAS6, Bld10, and POC1, which are conserved across eukaryotes, are expressed during spermatogenesis and required for this de novo biogenesis pathway. Our work supports a scenario where centriole biogenesis, while driven by conserved molecular modules, is more diverse than previously thought.

The 3D architecture and molecular foundations of de novo centriole assembly via bicentrioles

Centrioles are structurally conserved organelles, composing both centrosomes and cilia. In animal cycling cells, centrioles often form through a highly characterized process termed canonical duplication. However, a large diversity of eukaryotes assemble centrioles de novo through uncharacterized pathways. This unexplored diversity is key to understanding centriole assembly mechanisms and how they evolved to assist specific cellular functions. Here, we show that, during spermatogenesis of the bryophyte Physcomitrium patens, centrioles are born as a co-axially oriented centriole pair united by a cartwheel. Interestingly, we observe that these centrioles are twisted in opposite orientations. Microtubules emanate from the bicentrioles, which localize to the spindle poles during cell division. After their separation, the two resulting sister centrioles mature asymmetrically, elongating specific microtubule triplets and a naked cartwheel. Subsequently, two motile cilia are assembled that appear to alternate between different motility patterns. We further show that centriolar components SAS6, Bld10, and POC1, which are conserved across eukaryotes, are expressed during spermatogenesis and required for this de novo biogenesis pathway. Our work supports a scenario where centriole biogenesis, while driven by conserved molecular modules, is more diverse than previously thought.

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.

The Transport Behavior of a Biflagellated Microswimmer before and after Cargo Loading

The changes in the transport behavior of a microswimmer before and after cargo loading are crucial to understanding and control of the motion of a biohybrid microbot. In this work, we show the change in swimming behavior of biflagellated microalgae Chlamydomonas reinhardtii picking up a 4.5 μm polystyrene microbead upon collision. The microswimmer changed from linear forward motion into helical motion upon the attachment of the cargo and swam with a decreased swimming velocity. We revealed the helical motion of the microswimmer upon cargo loading due to suppression of flagella by image analysis of magnified time-lapse images of C. reinhardtii with one microbead attached at the anterior end (between the flagella). Furthered suppression on the flagellum imposed by the loading of the second cargo has led to increased oscillation per displacement traveled and decreased swimming velocity. Moreover, the microswimmer with a microbead attached at the posterior end swam with swimming velocity close to free swimming microalgae and did not exhibit helical swimming behavior. The experimental results and analysis showed that the loading location of the cargo has a great influence over the swimming behavior of the microswimmer. Furthermore, the work balance calculation and mathematical analysis based on Lighthill's model are well consistent with our experimental findings.

Temporal fluctuations in chemotaxis gain implement a simulated-tempering strategy for efficient navigation in complex environments

Bacterial chemotaxis is a major testing ground for systems biology, including the role of fluctuations and individual variation. Individual bacteria vary in their tumbling frequency and adaptation time. Recently, large cell-cell variation was also discovered in chemotaxis gain, which determines the sensitivity of the tumbling rate to attractant gradients. Variation in gain is puzzling, because low gain impairs chemotactic velocity. Here, we provide a functional explanation for gain variation by establishing a formal analogy between chemotaxis and algorithms for sampling probability distributions. We show that temporal fluctuations in gain implement simulated tempering, which allows sampling of attractant distributions with many local peaks. Periods of high gain allow bacteria to detect and climb gradients quickly, and periods of low gain allow them to move to new peaks. Gain fluctuations thus allow bacteria to thrive in complex environments, and more generally they may play an important functional role for organism navigation.

High-speed, three-dimensional imaging reveals chemotactic behaviour specific to human-infective Leishmania parasites

Cellular motility is an ancient eukaryotic trait, ubiquitous across phyla with roles in predator avoidance, resource access, and competition. Flagellar motility is seen in various parasitic protozoans, and morphological changes in flagella during the parasite life cycle have been observed. We studied the impact of these changes on motility across life cycle stages, and how such changes might serve to facilitate human infection. We used holographic microscopy to image swimming cells of different Leishmania mexicana life cycle stages in three dimensions. We find that the human-infective (metacyclic promastigote) forms display ‘run and tumble’ behaviour in the absence of stimulus, reminiscent of bacterial motion, and that they specifically modify swimming direction and speed to target host immune cells in response to a macrophage-derived stimulus. Non-infective (procyclic promastigote) cells swim more slowly, along meandering helical paths. These findings demonstrate adaptation of swimming phenotype and chemotaxis towards human cells.

Light-Powered Reactivation of Flagella and Contraction of Microtubule Networks: Toward Building an Artificial Cell

Artificial systems capable of self-sustained movement with self-sufficient energy are of high interest with respect to the development of many challenging applications, including medical treatments, but also technical applications. The bottom-up assembly of such systems in the context of synthetic biology is still a challenging task. In this work, we demonstrate the biocompatibility and efficiency of an artificial light-driven energy module and a motility functional unit by integrating light-switchable photosynthetic vesicles with demembranated flagella. The flagellar propulsion is coupled to the beating frequency, and dynamic ATP synthesis in response to illumination allows us to control beating frequency of flagella in a light-dependent manner. In addition, we verified the functionality of light-powered synthetic vesicles in in vitro motility assays by encapsulating microtubules assembled with force-generating kinesin-1 motors and the energy module to investigate the dynamics of a contractile filamentous network in cell-like compartments by optical stimulation. Integration of this photosynthetic system with various biological building blocks such as cytoskeletal filaments and molecular motors may contribute to the bottom-up synthesis of artificial cells that are able to undergo motor-driven morphological deformations and exhibit directional motion in a light-controllable fashion.

The bank of swimming organisms at the micron scale (BOSO-Micro)

Unicellular microscopic organisms living in aqueous environments outnumber all other creatures on Earth. A large proportion of them are able to self-propel in fluids with a vast diversity of swimming gaits and motility patterns. In this paper we present a biophysical survey of the available experimental data produced to date on the characteristics of motile behaviour in unicellular microswimmers. We assemble from the available literature empirical data on the motility of four broad categories of organisms: bacteria (and archaea), flagellated eukaryotes, spermatozoa and ciliates. Whenever possible, we gather the following biological, morphological, kinematic and dynamical parameters: species, geometry and size of the organisms, swimming speeds, actuation frequencies, actuation amplitudes, number of flagella and properties of the surrounding fluid. We then organise the data using the established fluid mechanics principles for propulsion at low Reynolds number. Specifically, we use theoretical biophysical models for the locomotion of cells within the same taxonomic groups of organisms as a means of rationalising the raw material we have assembled, while demonstrating the variability for organisms of different species within the same group. The material gathered in our work is an attempt to summarise the available experimental data in the field, providing a convenient and practical reference point for future studies.

Multi-ciliated microswimmers-metachronal coordination and helical swimming

The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number N (with [Formula: see text]) of cilia with length comparable to the body radius, is investigated by mesoscale hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e., the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity is found to increase with the cilia number N with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.

Effect of boundaries on noninteracting weakly active particles in different geometries

We study analytically how noninteracting weakly active particles, for which passive Brownian diffusion cannot be neglected and activity can be treated perturbatively, distribute and behave near boundaries in various geometries. In particular, we develop a perturbative approach for the model of active particles driven by an exponentially correlated random force (active Ornstein-Uhlenbeck particles). This approach involves a relatively simple expansion of the distribution in powers of the Péclet number and in terms of Hermite polynomials. We use this approach to cleanly formulate boundary conditions, which allows us to study weakly active particles in several geometries: confinement by a single wall or between two walls in 1D, confinement in a circular or wedge-shaped region in 2D, motion near a corrugated boundary, and, finally, absorption onto a sphere. We consider how quantities such as the density, pressure, and flow of the active particles change as we gradually increase the activity away from a purely passive system. These results for the limit of weak activity help us gain insight into how active particles behave in the presence of various types of boundaries.

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.