Coordinated beating of algal flagella is mediated by basal coupling

Biomimetic Synchronization in Biciliated Robots

Direct mechanical coupling is known to be critical for establishing synchronization among cilia. However, the actual role of the connections is still elusive-partly because controlled experiments in living samples are challenging. Here, we employ an artificial ciliary system to address this issue. Two cilia are formed by chains of self-propelling robots and anchored to a shared base so that they are purely mechanically coupled. The system mimics biological ciliary beating but allows fine control over the beating dynamics. With different schemes of mechanical coupling, artificial cilia exhibit rich motility patterns. Particularly, their synchronous beating display two distinct modes-analogous to those observed in C. reinhardtii, the biciliated model organism for studying synchronization. Close examination suggests that the system evolves towards the most dissipative mode. Using this guideline in both simulations and experiments, we are able to direct the system into a desired state by altering the modes' respective dissipation. Our results have significant implications in understanding the synchronization of cilia.

Data-driven classification of individual cells by their non-Markovian motion

We present a method to differentiate organisms solely by their motion based on the generalized Langevin equation (GLE) and use it to distinguish two different swimming modes of strongly confined unicellular microalgae Chlamydomonas reinhardtii. The GLE is a general model for active or passive motion of organisms and particles that can be derived from a time-dependent general many-body Hamiltonian and in particular includes non-Markovian effects (i.e., the trajectory memory of its past). We extract all GLE parameters from individual cell trajectories and perform an unbiased cluster analysis to group them into different classes. For the specific cell population employed in the experiments, the GLE-based assignment into the two different swimming modes works perfectly, as checked by control experiments. The classification and sorting of single cells and organisms is important in different areas; our method, which is based on motion trajectories, offers wide-ranging applications in biology and medicine.

Multiflagellate Swimming Controlled by Hydrodynamic Interactions

Many eukaryotic microorganisms propelled by multiple flagella can swim very rapidly with distinct gaits. Here, we model a three-dimensional mutiflagellate swimmer, resembling the microalgae. When the flagella are actuated synchronously, the swimming efficiency can be enhanced or reduced by interflagella hydrodynamic interactions (HIs), determined by the intrinsic tilting angle of the flagella. The asynchronous gait with a phase difference between neighboring flagella can reduce oscillatory motion via the basal mechanical coupling. In the presence of a spherical body, simulations taking into account the flagella-body interactions reveal the advantage of anterior configuration compared with posterior configuration, where in the latter case an optimal flagella number arises. Apart from understanding the role of HIs in the multiflagellate microorganisms, this work could also guide laboratory fabrications of novel microswimmers.

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.

Flow Physics Explains Morphological Diversity of Ciliated Organs

Organs that pump fluids by the coordinated beat of motile cilia through the lumen are integral to animal physiology. Such organs include the human airways, brain ventricles, and reproductive tracts. Although cilia organization and duct morphology vary drastically in the animal kingdom, ducts are typically classified as either carpet or flame designs. The reason behind this dichotomy and how duct design relates to fluid pumping remain unclear. Here, we demonstrate that two structural parameters -- lumen diameter and cilia-to-lumen ratio -- organize the observed duct diversity into a continuous spectrum that connects carpets to flames across all animal phyla. Using a unified fluid model, we show that carpet and flame designs maximize flow rate and pressure generation, respectively. We propose that convergence of ciliated organ designs follows functional constraints rather than phylogenetic distance, along with universal design rules for ciliary pumps.

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.

Mechanisms and functions of multiciliary coordination

Ciliated organisms are present in virtually every branch of the eukaryotic tree of life. In diverse systems, cilia operate in a coordinated manner to drive fluid flows, or even propel entire organisms. How do groups of motile cilia coordinate their activity within a cell or across a tissue to fulfil essential functions of life? In this review, we highlight the latest developments in our understanding of the mechanisms and functions of multiciliary coordination in diverse systems. We explore new and emerging trends in bioimaging, analytical, and computational methods, which together with their application in new model systems, have conspired to deliver important insights into one of the most fundamental questions in cellular dynamics.

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.

In vivo volumetric depth-resolved imaging of cilia metachronal waves using dynamic optical coherence tomography

Motile cilia are dynamic hair-like structures covering epithelial surfaces in multiple organs. The periodic coordinated beating of cilia creates waves propagating along the surface, known as the metachronal waves, which transport fluids and mucus along the epithelium. Motile ciliopathies result from disrupted coordinated cilia beating and are associated with serious clinical complications, including reproductive disorders. Despite the recognized clinical significance, research of cilia dynamics is extremely limited. Here, we present quantitative imaging of cilia metachronal waves volumetrically through tissue layers using dynamic optical coherence tomography (OCT). Our method relies on spatiotemporal mapping of the phase of intensity fluctuations in OCT images caused by the ciliary beating. We validated our new method ex vivo and implemented it in vivo to visualize cilia metachronal wave propagation within the mouse fallopian tube. This method can be extended to the assessment of physiological cilia function and ciliary dyskinesias in various organ systems, contributing to better management of pathologies associated with motile ciliopathies.

Active oscillations in microscale navigation

Living organisms routinely navigate their surroundings in search of better conditions, more food, or to avoid predators. Typically, animals do so by integrating sensory cues from the environment with their locomotor apparatuses. For single cells or small organisms that possess motility, fundamental physical constraints imposed by their small size have led to alternative navigation strategies that are specific to the microscopic world. Intriguingly, underlying these myriad exploratory behaviours or sensory functions is the onset of periodic activity at multiple scales, such as the undulations of cilia and flagella, the vibrations of hair cells, or the oscillatory shape modes of migrating neutrophils. Here, I explore oscillatory dynamics in basal microeukaryotes and hypothesize that these active oscillations play a critical role in enhancing the fidelity of adaptive sensorimotor integration.

Emerging roles for diguanylate cyclase during the evolution of soma in dictyostelia

BACKGROUND

Cyclic di-guanylate (c-di-GMP), synthesized by diguanylate cyclase, is a major second messenger in prokaryotes, where it triggers biofilm formation. The dictyostelid social amoebas acquired diguanylate cyclase (dgcA) by horizontal gene transfer. Dictyostelium discoideum (Ddis) in taxon group 4 uses c-di-GMP as a secreted signal to induce differentiation of stalk cells, the ancestral somatic cell type that supports the propagating spores. We here investigated how this role for c-di-GMP evolved in Dictyostelia by exploring dgcA function in the group 2 species Polysphondylium pallidum (Ppal) and in Polysphondylium violaceum (Pvio), which resides in a small sister clade to group 4.

RESULTS

Similar to Ddis, dgcA is upregulated after aggregation in Ppal and Pvio and predominantly expressed in the anterior region and stalks of emerging fruiting bodies. DgcA null mutants in Ppal and Pvio made fruiting bodies with very long and thin stalks and only few spores and showed delayed aggregation and larger aggregates, respectively. Ddis dgcA- cells cannot form stalks at all, but showed no aggregation defects. The long, thin stalks of Ppal and Pvio dgcA- mutants were also observed in acaA- mutants in these species. AcaA encodes adenylate cyclase A, which mediates the effects of c-di-GMP on stalk induction in Ddis. Other factors that promote stalk formation in Ddis are DIF-1, produced by the polyketide synthase StlB, low ammonia, facilitated by the ammonia transporter AmtC, and high oxygen, detected by the oxygen sensor PhyA (prolyl 4-hydroxylase). We deleted the single stlB, amtC and phyA genes in Pvio wild-type and dgcA- cells. Neither of these interventions affected stalk formation in Pvio wild-type and not or very mildly exacerbated the long thin stalk phenotype of Pvio dgcA- cells.

CONCLUSIONS

The study reveals a novel role for c-di-GMP in aggregation, while the reduced spore number in Pvio and Ppal dgcA- is likely an indirect effect, due to depletion of the cell pool by the extended stalk formation. The results indicate that in addition to c-di-GMP, Dictyostelia ancestrally used an as yet unknown factor for induction of stalk formation. The activation of AcaA by c-di-GMP is likely conserved throughout Dictyostelia.

Nonreciprocal interactions give rise to fast cilium synchronization in finite systems

Motile cilia beat in an asymmetric fashion in order to propel the surrounding fluid. When many cilia are located on a surface, their beating can synchronize such that their phases form metachronal waves. Here, we computationally study a model where each cilium is represented as a spherical particle, moving along a tilted trajectory with a position-dependent active driving force and a position-dependent internal drag coefficient. The model thus takes into account all the essential broken symmetries of the ciliary beat. We show that taking into account the near-field hydrodynamic interactions, the effective coupling between cilia even over an entire beating cycle can become nonreciprocal: The phase of a cilium is more strongly affected by an adjacent cilium on one side than by a cilium at the same distance in the opposite direction. As a result, synchronization starts from a seed at the edge of a group of cilia and propagates rapidly across the system, leading to a synchronization time that scales proportionally to the linear dimension of the system. We show that a ciliary carpet is characterized by three different velocities: the velocity of fluid transport, the phase velocity of metachronal waves, and the group velocity of order propagation. Unlike in systems with reciprocal coupling, boundary effects are not detrimental for synchronization, but rather enable the formation of the initial seed.

Robust acoustic trapping and perturbation of single-cell microswimmers illuminate three-dimensional swimming and ciliary coordination

We report a label-free acoustic microfluidic method to confine single, cilia-driven swimming cells in space without limiting their rotational degrees of freedom. Our platform integrates a surface acoustic wave (SAW) actuator and bulk acoustic wave (BAW) trapping array to enable multiplexed analysis with high spatial resolution and trapping forces that are strong enough to hold individual microswimmers. The hybrid BAW/SAW acoustic tweezers employ high-efficiency mode conversion to achieve submicron image resolution while compensating for parasitic system losses to immersion oil in contact with the microfluidic chip. We use the platform to quantify cilia and cell body motion for wildtype biciliate cells, investigating effects of environmental variables like temperature and viscosity on ciliary beating, synchronization, and three-dimensional helical swimming. We confirm and expand upon the existing understanding of these phenomena, for example determining that increasing viscosity promotes asynchronous beating. Motile cilia are subcellular organelles that propel microorganisms or direct fluid and particulate flow. Thus, cilia are critical to cell survival and human health. The unicellular alga Chlamydomonas reinhardtii is widely used to investigate the mechanisms underlying ciliary beating and coordination. However, freely swimming cells are difficult to image with sufficient resolution to capture cilia motion, necessitating that the cell body be held during experiments. Acoustic confinement is a compelling alternative to use of a micropipette, or to magnetic, electrical, and optical trapping that may modify the cells and affect their behavior. Beyond establishing our approach to studying microswimmers, we demonstrate a unique ability to mechanically perturb cells via rapid acoustic positioning.

Self-Oscillation and Synchronization Transitions in Elastoactive Structures

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

From a microscopic solution to a continuum description of active particles with a recoil interaction in one dimension

We consider a model system of persistent random walkers that can jam, pass through each other, or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we find that the stationary interparticle distribution functions are governed by an inhomogeneous fourth-order differential equation. Our main focus is on determining the boundary conditions that these distribution functions should satisfy. We find that these do not arise naturally from physical considerations, but they need to be carefully matched to functional forms that arise from the analysis of an underlying discrete process. The interparticle distribution functions, or their first derivatives, are generically found to be discontinuous at the boundaries.

3D-printed micrometer-scale wireless magnetic cilia with metachronal programmability

Biological cilia play essential roles in self-propulsion, food capture, and cell transportation by performing coordinated metachronal motions. Experimental studies to emulate the biological cilia metachronal coordination are challenging at the micrometer length scale because of current limitations in fabrication methods and materials. We report on the creation of wirelessly actuated magnetic artificial cilia with biocompatibility and metachronal programmability at the micrometer length scale. Each cilium is fabricated by direct laser printing a silk fibroin hydrogel beam affixed to a hard magnetic FePt Janus microparticle. The 3D-printed cilia show stable actuation performance, high temperature resistance, and high mechanical endurance. Programmable metachronal coordination can be achieved by programming the orientation of the identically magnetized FePt Janus microparticles, which enables the generation of versatile microfluidic patterns. Our platform offers an unprecedented solution to create bioinspired microcilia for programmable microfluidic systems, biomedical engineering, and biocompatible implants.

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.

From representations to servomechanisms to oscillators: my journey in the study of cognition

The study of comparative cognition bloomed in the 1970s and 1980s with a focus on representations in the heads of animals that undergird what animals can achieve. Even in action-packed domains such as navigation and spatial cognition, a focus on representations prevailed. In the 1990s, I suggested a conception of navigation in terms of navigational servomechanisms. A servomechanism can be said to aim for a goal, with deviations from the goal-directed path registering as an error. The error drives action to reduce the error in a negative-feedback loop. This loop, with the action reducing the very signal that drove action in the first place, is key to defining a servomechanism. Even though actions are crucial components of servomechanisms, my focus was on the representational component that encodes signals and evaluates errors. Recently, I modified and amplified this view in claiming that, in navigation, servomechanisms operate by modulating the performance of oscillators, endogenous units that produce periodic action. The pattern is found from bacteria travelling micrometres to sea turtles travelling thousands of kilometres. This pattern of servomechanisms working with oscillators is found in other realms of cognition and of life. I think that oscillators provide an effective way to organise an organism's own activities while servomechanisms provide an effective means to adjust to the organism's environment, including that of its own body.

Basal bodies bend in response to ciliary forces

Motile cilia beat with an asymmetric waveform consisting of a power stroke that generates a propulsive force and a recovery stroke that returns the cilium back to the start. Cilia are anchored to the cell cortex by basal bodies (BBs) that are directly coupled to the ciliary doublet microtubules (MTs). We find that, consistent with ciliary forces imposing on BBs, bending patterns in BB triplet MTs are responsive to ciliary beating. BB bending varies as environmental conditions change the ciliary waveform. Bending occurs where striated fibers (SFs) attach to BBs and mutants with short SFs that fail to connect to adjacent BBs exhibit abnormal BB bending, supporting a model in which SFs couple ciliary forces between BBs. Finally, loss of the BB stability protein Poc1, which helps interconnect BB triplet MTs, prevents the normal distributed BB and ciliary bending patterns. Collectively, BBs experience ciliary forces and manage mechanical coupling of these forces to their surrounding cellular architecture for normal ciliary beating.

Coordination of Cilia Movements in Multi-Ciliated Cells

Multiple motile cilia are formed at the apical surface of multi-ciliated cells in the epithelium of the oviduct or the fallopian tube, the trachea, and the ventricle of the brain. Those cilia beat unidirectionally along the tissue axis, and this provides a driving force for directed movements of ovulated oocytes, mucus, and cerebrospinal fluid in each of these organs. Furthermore, cilia movements show temporal coordination between neighboring cilia. To establish such coordination of cilia movements, cilia need to sense and respond to various cues, including the organ's orientation and movements of neighboring cilia. In this review, we discuss the mechanisms by which cilia movements of multi-ciliated cells are coordinated, focusing on planar cell polarity and the cytoskeleton, and highlight open questions for future research.

Spontaneous phase coordination and fluid pumping in model ciliary carpets

Ciliated tissues, such as in the mammalian lungs, brains, and reproductive tracts, are specialized to pump fluid. They generate flows by the collective activity of hundreds of thousands of individual cilia that beat in a striking metachronal wave pattern. Despite progress in analyzing cilia coordination, a general theory that links coordination and fluid pumping in the limit of large arrays of cilia remains lacking. Here, we conduct in silico experiments with thousands of hydrodynamically interacting cilia, and we develop a continuum theory in the limit of infinitely many independently beating cilia by combining tools from active matter and classical Stokes flow. We find, in both simulations and theory, that isotropic and synchronized ciliary states are unstable. Traveling waves emerge regardless of initial conditions, but the characteristics of the wave and net flows depend on cilia and tissue properties. That is, metachronal phase coordination is a stable global attractor in large ciliary carpets, even under finite perturbations to cilia and tissue properties. These results support the notion that functional specificity of ciliated tissues is interlaced with the tissue architecture and cilia beat kinematics and open up the prospect of establishing structure to function maps from cilium-level beat to tissue-level coordination and fluid pumping.

Gastrointestinal tract drug delivery using algae motors embedded in a degradable capsule

The use of micromotors for active drug delivery via oral administration has recently gained considerable interest. However, efficient motor-assisted delivery into the gastrointestinal (GI) tract remains challenging, owing to the short propulsion lifetime of currently used micromotor platforms. Here, we report on an efficient algae-based motor platform, which takes advantage of the fast and long-lasting swimming behavior of natural microalgae in intestinal fluid to prolong local retention within the GI tract. Fluorescent dye or cell membrane-coated nanoparticle functionalized algae motors were further embedded inside a pH-sensitive capsule to enhance delivery to the small intestines. In vitro, the algae motors displayed a constant motion behavior in simulated intestinal fluid after 12 hours of continuous operation. When orally administered in vivo into mice, the algae motors substantially improved GI distribution of the dye payload compared with traditional magnesium-based micromotors, which are limited by short propulsion lifetimes, and they also enhanced retention of a model chemotherapeutic payload in the GI tract compared with a passive nanoparticle formulation. Overall, combining the efficient motion and extended lifetime of natural algae-based motors with the protective capabilities of oral capsules results in a promising micromotor platform capable of achieving greatly improved cargo delivery in GI tissue for practical biomedical applications.

Intracellular connections between basal bodies promote the coordinated behavior of motile cilia

Hydrodynamic flow produced by multiciliated cells is critical for fluid circulation and cell motility. Hundreds of cilia beat with metachronal synchrony for fluid flow. Cilia-driven fluid flow produces extracellular hydrodynamic forces that cause neighboring cilia to beat in a synchronized manner. However, hydrodynamic coupling between neighboring cilia is not the sole mechanism that drives cilia synchrony. Cilia are nucleated by basal bodies (BBs) that link to each other and to the cell's cortex via BB-associated appendages. The intracellular BB and cortical network is hypothesized to synchronize ciliary beating by transmitting cilia coordination cues. The extent of intracellular ciliary connections and the nature of these stimuli remain unclear. Moreover, how BB connections influence the dynamics of individual cilia has not been established. We show by focused ion beam scanning electron microscopy imaging that cilia are coupled both longitudinally and laterally in the ciliate Tetrahymena thermophila by the underlying BB and cortical cytoskeletal network. To visualize the behavior of individual cilia in live, immobilized Tetrahymena cells, we developed Delivered Iron Particle Ubiety Live Light (DIPULL) microscopy. Quantitative and computer analyses of ciliary dynamics reveal that BB connections control ciliary waveform and coordinate ciliary beating. Loss of BB connections reduces cilia-dependent fluid flow forces.

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.

Ciliate cortical organization and dynamics for cell motility: Comparing ciliates and vertebrates

The generation of efficient fluid flow is crucial for organismal development and homeostasis, sexual reproduction, and motility. Multi-ciliated cells possess fields of motile cilia that beat in synchrony to propel fluid. Ciliary arrays are remarkably conserved in their organization and function. Ciliates have polarized multi-ciliary arrays (MCAs) to promote fluid flow for cell motility. The ciliate cortex is decorated with hundreds of basal bodies (BB) forming linear rows along the cell's anterior-posterior axis. BBs scaffold and position cilia to form the organized ciliary array. Nascent BBs assemble at the base of BBs. As nascent BBs mature, they integrate into the cortical BB and cytoskeletal network and nucleate their own cilium. The organization of MCAs is balanced between cortical stability and cortical dynamism. The cortical cytoskeletal network both establishes and maintains a stable organization of the MCA in the face of mechanical forces exerted by ciliary beating. At the same time, MCA organization is plastic, such that it remodels for optimal ciliary mobility during development and in response to environmental conditions. Such plasticity promotes effective feeding and ecological behavior required for these organisms. Together, these properties allow an organism to effectively sense, adapt to, and move through its environment.

Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics

Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.

Elastohydrodynamic Synchronization of Rotating Bacterial Flagella

To rotate continuously without jamming, the flagellar filaments of bacteria need to be locked in phase. While several models have been proposed for eukaryotic flagella, the synchronization of bacterial flagella is less well understood. Starting from a reduced model of flexible and hydrodynamically coupled bacterial flagella, we rigorously coarse grain the equations of motion using the method of multiple scales, and hence show that bacterial flagella generically synchronize to zero phase difference via an elastohydrodynamic mechanism. Remarkably, the far-field rate of synchronization is maximized at an intermediate value of elastic compliance, with surprising implications for bacteria.

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.

Synchronization and Enhanced Catalysis of Mechanically Coupled Enzymes

We examine the stochastic dynamics of two enzymes that are mechanically coupled to each other, e.g., through an elastic substrate or a fluid medium. The enzymes undergo conformational changes during their catalytic cycle, which itself is driven by stochastic steps along a biased chemical free energy landscape. We find conditions under which the enzymes can synchronize their catalytic steps, and discover that the coupling can lead to a significant enhancement in their overall catalytic rate. Both effects can be understood as arising from a global bifurcation in the underlying dynamical system at sufficiently strong coupling. Our findings suggest that, despite their molecular scale, enzymes can be cooperative and improve their performance in metabolic clusters.

Ferroptosis in liver disease: new insights into disease mechanisms

Characterized by excessive iron accumulation and lipid peroxidation, ferroptosis is a novel form of iron-dependent cell death, which is morphologically, genetically, and biochemically distinct from other well-known cell death. In recent years, ferroptosis has been quickly gaining attention in the field of liver diseases, as the liver is predisposed to oxidative injury and generally, excessive iron accumulation is a primary characteristic of most major liver diseases. In the current review, we first delineate three cellular defense mechanisms against ferroptosis (GPx4 in the mitochondria and cytosol, FSP1 on plasma membrane, and DHODH in mitochondria), along with four canonical modulators of ferroptosis (system Xc⁻, nuclear factor erythroid 2-related factor 2, p53, and GTP cyclohydrolase-1). Next, we review recent progress of ferroptosis studies delineating molecular mechanisms underlying the pathophysiology of several common liver diseases including ischemia/reperfusion-related injury (IRI), nonalcoholic fatty liver disease (NAFLD), alcoholic liver disease (ALD), hemochromatosis (HH), drug-induced liver injury (DILI), and hepatocellular carcinoma (HCC). Furthermore, we also highlight both challenges and promises that emerged from recent studies that should be addressed and pursued in future investigations before ferroptosis regulation could be adopted as an effective therapeutic target in clinical practice.

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.

A minimal robophysical model of quadriflagellate self-propulsion

Locomotion at the microscale is remarkably sophisticated. Microorganisms have evolved diverse strategies to move within highly viscous environments, using deformable, propulsion-generating appendages such as cilia and flagella to drive helical or undulatory motion. In single-celled algae, these appendages can be arranged in different ways around an approximately 10 μm long cell body, and coordinated in distinct temporal patterns. Inspired by the observation that some quadriflagellates (bearing four flagella) have an outwardly similar morphology and flagellar beat pattern, yet swim at different speeds, this study seeks to determine whether variations in swimming performance could arise solely from differences in swimming gait. Robotics approaches are particularly suited to such investigations, where the phase relationships between appendages can be readily manipulated. Here, we developed autonomous, algae-inspired robophysical models that can self-propel in a viscous fluid. These macroscopic robots (length and width = 8.5 cm, height = 2 cm) have four independently actuated 'flagella' (length = 13 cm) that oscillate under low-Reynolds number conditions (Re∼O(10-1)). We tested the swimming performance of these robot models with appendages arranged two distinct configurations, and coordinated in three distinct gaits. The gaits, namely the pronk, the trot, and the gallop, correspond to gaits adopted by distinct microalgal species. When the appendages are inserted perpendicularly around a central 'body', the robot achieved a net performance of 0.15-0.63 body lengths per cycle, with the trot gait being the fastest. Robotic swimming performance was found to be comparable to that of the algal microswimmers across all gaits. By creating a minimal robot that can successfully reproduce cilia-inspired drag-based swimming, our work paves the way for the design of next-generation devices that have the capacity to autonomously navigate aqueous environments.

The structure and function of centriolar rootlets

To gain a holistic understanding of cellular function, we must understand not just the role of individual organelles, but also how multiple macromolecular assemblies function collectively. Centrioles produce fundamental cellular processes through their ability to organise cytoskeletal fibres. In addition to nucleating microtubules, centrioles form lesser-known polymers, termed rootlets. Rootlets were identified over a 100 years ago and have been documented morphologically since by electron microscopy in different eukaryotic organisms. Rootlet-knockout animals have been created in various systems, providing insight into their physiological functions. However, the precise structure and function of rootlets is still enigmatic. Here, I consider common themes of rootlet function and assembly across diverse cellular systems. I suggest that the capability of rootlets to form physical links from centrioles to other cellular structures is a general principle unifying their functions in diverse cells and serves as an example of how cellular function arises from collective organellar activity.

Conditions for metachronal coordination in arrays of model cilia

Motile cilia can coordinate with each other to beat in the form of a metachronal wave, which can facilitate the self-propulsion of microorganisms such as Paramecium and can also be used for fluid transport such as mucus removal in trachea. How can we predict the collective behavior of arrays of many cilia coordinated by hydrodynamic interactions, and in particular, the properties of the emerging metachronal waves, from the single-cilium characteristics? We address this question using a bottom-up coarse-graining approach and present results that contribute to understanding how the dynamical self-organization of ciliary arrays can be controlled, which can have significant biological, medical, and engineering implications.

On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse graining. We uncover the criteria that control the selection of frequency and wave vector of stable metachronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of a single cilium, as well as the geometric properties of the array. We perform agent-based numerical simulations of arrays of cilia with hydrodynamic interactions and find quantitative agreement with the predictions of the analytical framework. Our work sheds light on the question of how the collective properties of beating cilia can be determined using information about the individual units and, as such, exemplifies a bottom-up study of a rich active matter system.

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.

Metachronal motion across scales: current challenges and future directions

Metachronal motion is used across a wide range of organisms for a diverse set of functions. However, despite its ubiquity, analysis of this behavior has been difficult to generalize across systems. Here we provide an overview of known commonalities and differences between systems that use metachrony to generate fluid flow. We also discuss strategies for standardizing terminology and defining future investigative directions that are analogous to other established subfields of biomechanics. Lastly, we outline key challenges that are common to many metachronal systems, opportunities that have arisen due to the advent of new technology (both experimental and computational), and next steps for community development and collaboration across the nascent network of metachronal researchers.

Analysis of biological noise in the flagellar length control system

Any proposed mechanism for organelle size control should be able to account not only for average size but also for the variation in size. We analyzed cell-to-cell variation and within-cell variation of length for the two flagella in Chlamydomonas, finding that cell-to-cell variation is dominated by cell size, whereas within-cell variation results from dynamic fluctuations. Fluctuation analysis suggests tubulin assembly is not directly coupled with intraflagellar transport (IFT) and that the observed length fluctuations reflect tubulin assembly and disassembly events involving large numbers of tubulin dimers. Length variation is increased in long-flagella mutants, an effect consistent with theoretical models for flagellar length regulation. Cells with unequal flagellar lengths show impaired swimming but improved gliding, raising the possibility that cells have evolved mechanisms to tune biological noise in flagellar length. Analysis of noise at the level of organelle size provides a way to probe the mechanisms determining cell geometry.

Heme-binding protein CYB5D1 is a radial spoke component required for coordinated ciliary beating

Coordinated beating is crucial for the function of multiple cilia. However, the molecular mechanism is poorly understood. Here, we characterize a conserved ciliary protein CYB5D1 with a heme-binding domain and a cordon-bleu ubiquitin-like domain. Mutation or knockdown of Cyb5d1 in zebrafish impaired coordinated ciliary beating in the otic vesicle and olfactory epithelium. Similarly, the two flagella of an insertional mutant of the CYB5D1 ortholog in Chlamydomonas (Crcyb5d1) showed an uncoordinated pattern due to a defect in the cis-flagellum. Biochemical analyses revealed that CrCYB5D1 is a radial spoke stalk protein that binds heme only under oxidizing conditions. Lack of CrCYB5D1 resulted in a reductive shift in flagellar redox state and slowing down of the phototactic response. Treatment of Crcyb5d1 with oxidants restored coordinated flagellar beating. Taken together, these data suggest that CrCYB5D1 may integrate environmental and intraciliary signals and regulate the redox state of cilia, which is crucial for the coordinated beating of multiple cilia.

Energetics of synchronization for model flagella and cilia

Synchronization is often observed in the swimming of flagellated cells, either for multiple appendages on the same organism or between the flagella of nearby cells. Beating cilia are also seen to synchronize their dynamics. In 1951, Taylor showed that the observed in-phase beating of the flagella of coswimming spermatozoa was consistent with minimization of the energy dissipated in the surrounding fluid. Here we revisit Taylor's hypothesis for three models of flagella and cilia: (1) Taylor's waving sheets with both longitudinal and transverse modes, as relevant for flexible flagella, (2) spheres orbiting above a no-slip surface to model interacting flexible cilia, and (3) whirling rods above a no-slip surface to address the interaction of nodal cilia. By calculating the flow fields explicitly, we show that the rate of working of the model flagella or cilia is minimized in our three models for (1) a phase difference depending on the separation of the sheets and precise waving kinematics, (2) in-phase or opposite-phase motion depending on the relative position and orientation of the spheres, and (3) in-phase whirling of the rods. These results will be useful in future models probing the dynamics of synchronization in these setups.

Origins of eukaryotic excitability

All living cells interact dynamically with a constantly changing world. Eukaryotes, in particular, evolved radically new ways to sense and react to their environment. These advances enabled new and more complex forms of cellular behaviour in eukaryotes, including directional movement, active feeding, mating, and responses to predation. But what are the key events and innovations during eukaryogenesis that made all of this possible? Here we describe the ancestral repertoire of eukaryotic excitability and discuss five major cellular innovations that enabled its evolutionary origin. The innovations include a vastly expanded repertoire of ion channels, the emergence of cilia and pseudopodia, endomembranes as intracellular capacitors, a flexible plasma membrane and the relocation of chemiosmotic ATP synthesis to mitochondria, which liberated the plasma membrane for more complex electrical signalling involved in sensing and reacting. We conjecture that together with an increase in cell size, these new forms of excitability greatly amplified the degrees of freedom associated with cellular responses, allowing eukaryotes to vastly outperform prokaryotes in terms of both speed and accuracy. This comprehensive new perspective on the evolution of excitability enriches our view of eukaryogenesis and emphasizes behaviour and sensing as major contributors to the success of eukaryotes. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Control of Helical Navigation by Three-Dimensional Flagellar Beating

Helical swimming is a ubiquitous strategy for motile cells to generate self-gradients for environmental sensing. The model biflagellate Chlamydomonas reinhardtii rotates at a constant 1-2 Hz as it swims, but the mechanism is unclear. Here, we show unequivocally that the rolling motion derives from a persistent, nonplanar flagellar beat pattern. This is revealed by high-speed imaging and micromanipulation of live cells. We construct a fully 3D model to relate flagellar beating directly to the free-swimming trajectories. For realistic geometries, the model reproduces both the sense and magnitude of the axial rotation of live cells. We show that helical swimming requires further symmetry breaking between the two flagella. These functional differences underlie all tactic responses, particularly phototaxis. We propose a control strategy by which cells steer toward or away from light by modulating the sign of biflagellar dominance.

Resistive force theory and wave dynamics in swimming flagellar apparatus isolated from C. reinhardtii

Cilia-driven motility and fluid transport are ubiquitous in nature and essential for many biological processes, including swimming of eukaryotic unicellular organisms, mucus transport in airway apparatus or fluid flow in the brain. The-biflagellated micro-swimmer Chlamydomonas reinhardtii is a model organism to study the dynamics of flagellar synchronization. Hydrodynamic interactions, intracellular mechanical coupling or cell body rocking is believed to play a crucial role in the synchronization of flagellar beating in green algae. Here, we use freely swimming intact flagellar apparatus isolated from a wall-less strain of Chlamydomonas to investigate wave dynamics. Our analysis on phase coordinates shows that when the frequency difference between the flagella is high (10-41% of the mean), neither mechanical coupling via basal body nor hydrodynamics interactions are strong enough to synchronize two flagella, indicating that the beating frequency is perhaps controlled internally by the cell. We also examined the validity of resistive force theory for a flagellar apparatus swimming freely in the vicinity of a substrate and found quantitative agreement between the experimental data and simulations with a drag anisotropy of ratio 2. Finally, using a simplified wave form, we investigated the influence of phase and frequency differences, intrinsic curvature and wave amplitude on the swimming trajectory of flagellar apparatus. Our analysis shows that by controlling the phase or frequency differences between two flagella, steering can occur.

Hydrodynamic synchronization in strong confinement

Cellular appendages conferring motility, such as flagella and cilia, are known to synchronise their periodic beats. The origin of synchronization is a combination of long-range hydrodynamic interactions with physical mechanisms allowing the phases of these biological oscillators to evolve. Two of such mechanisms have been identified by previous work, the elastic compliance of the periodic orbit or oscillations driven by phase-dependent biological forcing, both of which can lead generically to stable phase locking. In order to help uncover the physical mechanism for hydrodynamic synchronization most essential overall in biology, we theoretically investigate in this paper the effect of strong confinement on the effectiveness of hydrodynamic synchronization. Following past work, we use minimal models of cilia where appendages are modeled as rigid spheres forced to move along circular trajectories near a rigid surface. Strong confinement is modeled by adding a second nearby surface, parallel to the first one, where the distance between the surfaces is much smaller than the typical distance between the cilia, which results in a qualitative change in the nature of hydrodynamic interactions. We calculate separately the impact of hydrodynamic confinement on the synchronization dynamics of the elastic compliance and the force modulation mechanisms and compare our results to the usual case with a single surface. Applying our results to the biologically relevant situation of nodal cilia, we show that force modulation is a mechanism that leads to phase-locked states under strong confinement that are very similar to those without confinement as a difference with the elastic compliance mechanism. Our results point therefore to the robustness of force modulation for synchronization, an important feature for biological dynamics that therefore suggests it could be the most essential physical mechanism overall in arrays of nodal cilia. We further examine the distinct biologically relevant situation of primary cilia and show in that case that the difference in robustness of the mechanisms is not as pronounced but still favors the force modulation.

Foraging trade-offs, flagellar arrangements, and flow architecture of planktonic protists

Unicellular flagellated protists are a key element in aquatic microbial food webs. They all use flagella to swim and to generate feeding currents to encounter prey and enhance nutrient uptake. At the same time, the beating flagella create flow disturbances that attract flow-sensing predators. Protists have highly diverse flagellar arrangements in terms of number of flagella and their position, beat pattern, and kinematics, but it is unclear how the various arrangements optimize the fundamental trade-off between resource acquisition and predation risk. Here we describe the near-cell flow fields produced by 15 species and demonstrate consistent relationships between flagellar arrangement and swimming speed and between flagellar arrangement and flow architecture, and a trade-off between resource acquisition and predation risk. The flow fields fall in categories that are qualitatively described by simple point force models that include the drag force of the moving cell body and the propulsive forces of the flagella. The trade-off between resource acquisition and predation risk varies characteristically between flow architectures: Flagellates with multiple flagella have higher predation risk relative to their clearance rate compared to species with only one active flagellum, with the exception of the highly successful dinoflagellates that have simultaneously achieved high clearance rates and stealth behavior due to a unique flagellar arrangement. Microbial communities are shaped by trade-offs and environmental constraints, and a mechanistic explanation of foraging trade-offs is a vital part of understanding the eukaryotic communities that form the basis of pelagic food webs.

Intracellular coupling modulates biflagellar synchrony

Beating flagella exhibit a variety of synchronization modes. This synchrony has long been attributed to hydrodynamic coupling between the flagella. However, recent work with flagellated algae indicates that a mechanism internal to the cell, through the contractile fibres connecting the flagella basal bodies, must be at play to actively modulate flagellar synchrony. Exactly how basal coupling mediates flagellar coordination remains unclear. Here, we examine the role of basal coupling in the synchronization of the model biflagellate Chlamydomonas reinhardtii using a series of mathematical models of decreasing levels of complexity. We report that basal coupling is sufficient to achieve inphase, antiphase and bistable synchrony, even in the absence of hydrodynamic coupling and flagellar compliance. These modes can be reached by modulating the activity level of the individual flagella or the strength of the basal coupling. We observe a slip mode when allowing for differential flagellar activity, just as in experiments with live cells. We introduce a dimensionless ratio of flagellar activity to basal coupling that is predictive of the mode of synchrony. This ratio allows us to query biological parameters which are not yet directly measurable experimentally. Our work shows a concrete route for cells to actively control the synchronization of their flagella.