Swimming like algae: biomimetic soft artificial cilia

Advancements in materials, manufacturing, propulsion and localization: propelling soft robotics for medical applications

Soft robotics is an emerging field showing immense potential for biomedical applications. This review summarizes recent advancements in soft robotics for in vitro and in vivo medical contexts. Their inherent flexibility, adaptability, and biocompatibility enable diverse capabilities from surgical assistance to minimally invasive diagnosis and therapy. Intelligent stimuli-responsive materials and bioinspired designs are enhancing functionality while improving biocompatibility. Additive manufacturing techniques facilitate rapid prototyping and customization. Untethered chemical, biological, and wireless propulsion methods are overcoming previous constraints to access new sites. Meanwhile, advances in tracking modalities like computed tomography, fluorescence and ultrasound imaging enable precision localization and control enable in vivo applications. While still maturing, soft robotics promises more intelligent, less invasive technologies to improve patient care. Continuing research into biocompatibility, power supplies, biomimetics, and seamless localization will help translate soft robots into widespread clinical practice.

Fabrication, control, and modeling of robots inspired by flagella and cilia

Flagella and cilia are slender structures that serve important functionalities in the microscopic world through their locomotion induced by fluid and structure interaction. With recent developments in microscopy, fabrication, biology, and modeling capability, robots inspired by the locomotion of these organelles in low Reynolds number flow have been manufactured and tested on the micro-and macro-scale, ranging from medicalin vivomicrobots, microfluidics to macro prototypes. We present a collection of modeling theories, control principles, and fabrication methods for flagellated and ciliary robots.

Morphological Control of Cilia-Inspired Asymmetric Movements Using Nonlinear Soft Inflatable Actuators

Soft robotic systems typically follow conventional control schemes, where actuators are supplied with dedicated inputs that are regulated through software. However, in recent years an alternative trend is being explored, where the control architecture can be simplified by harnessing the passive mechanical characteristics of the soft robotic system. This approach is named “morphological control”, and it can be used to decrease the number of components (tubing, valves and regulators) required by the controller. In this paper, we demonstrate morphological control of bio-inspired asymmetric motions for systems of soft bending actuators that are interconnected with passive flow restrictors. We introduce bending actuators consisting out of a cylindrical latex balloon in a flexible PVC shell. By tuning the radii of the tube and the shell, we obtain a nonlinear relation between internal pressure and volume in the actuator with a peak and valley in pressure. Because of the nonlinear characteristics of the actuators, they can be assembled in a system with a single pressure input where they bend in a discrete, preprogrammed sequence. We design and analyze two such systems inspired by the asymmetric movements of biological cilia. The first replicates the swept area of individual cilia, having a different forward and backward stroke, and the second generates a travelling wave across an array of cilia.

Shape-programmable artificial cilia for microfluidics

The artificial ciliary motion has been known not to be hydrodynamically optimal, limiting their associated applications in the microscale flow domain. One of the major hurdles of contemporary artificial cilia is its structural rigidity, which restricts their flexibility. To address this issue, this work proposed a shape-programmable artificial cilia design with distinctive polydimethylsiloxane (PDMS) and magnetic segments distributed throughout the structure, which provided precise control for time-spatial modulation of the whole artificial cilia structure under external magnetic actuation. For the fabrication of the proposed multi-segment artificial cilia, a facile microfabrication process with stepwise mold blocking followed by the PDMS and magnetic composite casting was adopted. The hydrodynamic analysis further elucidated that the proposed artificial cilia beating induced significant flow disturbance within the flow field, and the associated application was demonstrated through an efficient mixing operation.

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Fabrication of artificial cilia was conducted through micromilling and casting methods.

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The weighted index was correlated to the bending angles of artificial cilia.

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Hydrodynamic analysis of artificial cilia was performed through the μPIV analysis.

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A significant improvement in mixing performance was achieved in few seconds.

The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis

We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed 'spinning lasso', arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.

Metachronal patterns in artificial cilia for low Reynolds number fluid propulsion

Cilia are hair-like organelles, present in arrays that collectively beat to generate flow. Given their small size and consequent low Reynolds numbers, asymmetric motions are necessary to create a net flow. Here, we developed an array of six soft robotic cilia, which are individually addressable, to both mimic nature's symmetry-breaking mechanisms and control asymmetries to study their influence on fluid propulsion. Our experimental tests are corroborated with fluid dynamics simulations, where we find a good agreement between both and show how the kymographs of the flow are related to the phase shift of the metachronal waves. Compared to synchronous beating, we report a 50% increase of net flow speed when cilia move in an antiplectic wave with phase shift of -π/3 and a decrease for symplectic waves. Furthermore, we observe the formation of traveling vortices in the direction of the wave when metachrony is applied.

Advanced Actuator Materials Powered by Biomimetic Helical Fiber Topologies

Helical constructs are ubiquitous in nature at all size domains, from molecular to macroscopic. The helical topology confers unique mechanical functions that activate certain phenomena, such as twining vines and vital cellular functions like the folding and packing of DNA into chromosomes. The understanding of active mechanical processes in plants, certain musculature in animals, and some biochemical processes in cells provides insight into the versatility of the helix. Most of these natural systems consist of helically oriented filaments embedded in a compliant matrix. In some cases, the matrix can change volume and in others the filaments can contract and the matrix is passive. In both cases, the helically arranged fibers determine the overall shape change with a great variety of responses involving length contraction/elongation, twisting, bending, and coiling. Synthetic actuator materials and systems that employ helical topologies have been described recently and demonstrate many fascinating and complex shape changes. However, significant new opportunities exist to mimic some of the most remarkable actions in nature, including the Vorticella's coiling stalk and DNA's supercoils, in the quest for superior artificial muscles.

Bioinspired reorientation strategies for application in micro/nanorobotic control

Engineers have recently been inspired by swimming methodologies of microorganisms in creating micro-/nanorobots for biomedical applications. Future medicine may be revolutionized by the application of these small machines in diagnosing, monitoring, and treating diseases. Studies over the past decade have often concentrated on propulsion generation. However, there are many other challenges to address before the practical use of robots at the micro-/nanoscale. The control and reorientation ability of such robots remain as some of these challenges. This paper reviews the strategies of swimming microorganisms for reorientation, including tumbling, reverse and flick, direction control of helical-path swimmers, by speed modulation, using complex flagella, and the help of mastigonemes. Then, inspired by direction change in microorganisms, methods for orientation control for microrobots and possible directions for future studies are discussed. Further, the effects of solid boundaries on the swimming trajectories of microorganisms and microrobots are examined. In addition to propulsion systems for artificial microswimmers, swimming microorganisms are promising sources of control methodologies at the micro-/nanoscale.

Oscillations of a cantilevered micro beam driven by a viscoelastic flow instability

The interaction of flexible structures with viscoelastic flows can result in very rich dynamics. In this paper, we present the results of the interactions between the flow of a viscoelastic polymer solution and a cantilevered beam in a confined microfluidic geometry. Cantilevered beams with varying length and flexibility were studied. With increasing flow rate and Weissenberg number, the flow transitioned from a fore-aft symmetric flow to a stable detached vortex upstream of the beam, to a time-dependent unstable vortex shedding. The shedding of the unstable vortex upstream of the beam imposed a time-dependent drag force on the cantilevered beam resulting in flow-induced beam oscillations. The oscillations of the flexible beam were classified into two distinct regimes: a regime with a clear single vortex shedding from upstream of the beam resulting in a sinusoidal beam oscillation pattern with the frequency of oscillation increasing monotonically with Weissenberg number, and a regime at high Weissenberg numbers characterized by 3D viscoelastic instabilities where the frequency of oscillations plateaued. The critical onset of the flow transitions, the mechanism of vortex shedding and the dynamics of the cantilevered beam response are presented in detail here as a function of beam flexibility and flow viscoelasticity.

Design and Modeling of a New Biomimetic Soft Robotic Jellyfish Using IPMC-Based Electroactive Polymers

Smart materials and soft robotics have been seen to be particularly well-suited for developing biomimetic devices and are active fields of research. In this study, the design and modeling of a new biomimetic soft robot is described. Initial work was made in the modeling of a biomimetic robot based on the locomotion and kinematics of jellyfish. Modifications were made to the governing equations for jellyfish locomotion that accounted for geometric differences between biology and the robotic design. In particular, the capability of the model to account for the mass and geometry of the robot design has been added for better flexibility in the model setup. A simple geometrically defined model is developed and used to show the feasibility of a proposed biomimetic robot under a prescribed geometric deformation to the robot structure. A more robust mechanics model is then developed which uses linear beam theory is coupled to an equivalent circuit model to simulate actuation of the robot with ionic polymer-metal composite (IPMC) actuators. The mechanics model of the soft robot is compared to that of the geometric model as well as biological jellyfish swimming to highlight its improved efficiency. The design models are characterized against a biological jellyfish model in terms of propulsive efficiency. Using the mechanics model, the locomotive energetics as modeled in literature on biological jellyfish are explored. Locomotive efficiency and cost as a function of swimming cycles are examined for various swimming modes developed, followed by an analysis of the initial transient and steady-state swimming velocities. Applications for fluid pumping or thrust vectoring utilizing the same basic robot design are also proposed. The new design shows a clear advantage over its purely biological counterpart for a soft-robot, with the newly proposed biomimetic swimming mode offering enhanced swimming efficiency and steady-state velocities for a given size and volume exchange.

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: Implications for the hydrodynamics of an active microswimmer near an elastic interface

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future for biomedical and technological applications. These microswimmers move autonomously through aqueous media, where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than those due to shear resistance. Bending can enhance (suppress) the velocities resulting from higher-order singularities whereas the shear related contribution decreases (increases) the velocities. Most prominently, we find that near an elastic interface of only energetic resistance toward shear deformation, such as that of an elastic capsule designed for drug delivery, a swimming bacterium undergoes rotation of the same sense as observed near a no-slip wall. In contrast to that, near an interface of only energetic resistance toward bending, such as that of a fluid vesicle or liposome, we find a reversed sense of rotation. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

From isolated structures to continuous networks: A categorization of cytoskeleton-based motile engineered biological microstructures

As technology at the small scale is advancing, motile engineered microstructures are becoming useful in drug delivery, biomedicine, and lab-on-a-chip devices. However, traditional engineering methods and materials can be inefficient or functionally inadequate for small-scale applications. Increasingly, researchers are turning to the biology of the cytoskeleton, including microtubules, actin filaments, kinesins, dyneins, myosins, and associated proteins, for both inspiration and solutions. They are engineering structures with components that range from being entirely biological to being entirely synthetic mimics of biology and on scales that range from isotropic continuous networks to single isolated structures. Motile biological microstructures trace their origins from the development of assays used to study the cytoskeleton to the array of structures currently available today. We define 12 types of motile biological microstructures, based on four categories: entirely biological, modular, hybrid, and synthetic, and three scales: networks, clusters, and isolated structures. We highlight some key examples, the unique functionalities, and the potential applications of each microstructure type, and we summarize the quantitative models that enable engineering them. By categorizing the diversity of motile biological microstructures in this way, we aim to establish a framework to classify these structures, define the gaps in current research, and spur ideas to fill those gaps. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Nanotechnology Approaches to Biology > Cells at the Nanoscale Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Therapeutic Approaches and Drug Discovery > Emerging Technologies.

Actuation of chitosan-aptamer nanobrush borders for pathogen sensing

We demonstrate a sensing mechanism for rapid detection of Listeria monocytogenes in food samples using the actuation of chitosan-aptamer nanobrush borders. The bio-inspired soft material and sensing strategy mimic natural symbiotic systems, where low levels of bacteria are selectively captured from complex matrices. To engineer this biomimetic system, we first develop reduced graphene oxide/nanoplatinum (rGO-nPt) electrodes, and characterize the fundamental electrochemical behavior in the presence and absence of chitosan nanobrushes during actuation (pH-stimulated osmotic swelling). We then characterize the electrochemical behavior of the nanobrush when receptors (antibodies or DNA aptamers) are conjugated to the surface. Finally, we test various techniques to determine the most efficient capture strategy based on nanobrush actuation, and then apply the biosensors in a food product. Maximum cell capture occurs when aptamers conjugated to the nanobrush bind cells in the extended conformation (pH < 6), followed by impedance measurement in the collapsed nanobrush conformation (pH > 6). The aptamer-nanobrush hybrid material was more efficient than the antibody-nanobrush material, which was likely due to the relatively high adsorption capacity for aptamers. The biomimetic material was used to develop a rapid test (17 min) for selectively detecting L. monocytogenes at concentrations ranging from 9 to 107 CFU mL-1 with no pre-concentration, and in the presence of other Gram-positive cells (Listeria innocua and Staphylococcus aureus). Use of this bio-inspired material is among the most efficient for L. monocytogenes sensing to date, and does not require sample pretreatment, making nanobrush borders a promising new material for rapid pathogen detection in food.

A Parallel Modular Biomimetic Cilia Sorting Platform

The aquatic unicellular organism Paramecium caudatum uses cilia to swim around its environment and to graze on food particles and bacteria. Paramecia use waves of ciliary beating for locomotion, intake of food particles and sensing. There is some evidence that Paramecia pre-sort food particles by discarding larger particles, but intake the particles matching their mouth cavity. Most prior attempts to mimic cilia-based manipulation merely mimicked the overall action rather than the beating of cilia. The majority of massive-parallel actuators are controlled by a central computer; however, a distributed control would be far more true-to-life. We propose and test a distributed parallel cilia platform where each actuating unit is autonomous, yet exchanging information with its closest neighboring units. The units are arranged in a hexagonal array. Each unit is a tileable circuit board, with a microprocessor, color-based object sensor and servo-actuated biomimetic cilia actuator. Localized synchronous communication between cilia allowed for the emergence of coordinated action, moving different colored objects together. The coordinated beating action was capable of moving objects up to 4 cm/s at its highest beating frequency; however, objects were moved at a speed proportional to the beat frequency. Using the local communication, we were able to detect the shape of objects and rotating an object using edge detection was performed; however, lateral manipulation using shape information was unsuccessful.

Acoustic Actuation of in situ Fabricated Artificial Cilia

We present on-chip acoustic actuation of in situ fabricated artificial cilia. Arrays of cilia structures are UV polymerized inside a microfluidic channel using a photocurable polyethylene glycol (PEG) polymer solution and photomasks. During polymerization, cilia structures are attached to a silane treated glass surface inside the microchannel. Then, the cilia structures are actuated using acoustic vibrations at 4.6 kHz generated by piezo transducers. As a demonstration of a practical application, DI water and fluorescein dye solutions are mixed inside a microfluidic channel. Using pulses of acoustic excitations, and locally fabricated cilia structures within a certain region of the microchannel, a waveform of mixing behavior is obtained. This result illustrates one potential application wherein researchers can achieve spatiotemporal control of biological microenvironments in cell stimulation studies. These acoustically actuated, in situ fabricated, cilia structures can be used in many on-chip applications in biological, chemical and engineering studies.

Soft robotic ventricular assist device with septal bracing for therapy of heart failure

Previous soft robotic ventricular assist devices have generally targeted biventricular heart failure and have not engaged the interventricular septum that plays a critical role in blood ejection from the ventricle. We propose implantable soft robotic devices to augment cardiac function in isolated left or right heart failure by applying rhythmic loading to either ventricle. Our devices anchor to the interventricular septum and apply forces to the free wall of the ventricle to cause approximation of the septum and free wall in systole and assist with recoil in diastole. Physiological sensing of the native hemodynamics enables organ-in-the-loop control of these robotic implants for fully autonomous augmentation of heart function. The devices are implanted on the beating heart under echocardiography guidance. We demonstrate the concept on both the right and the left ventricles through in vivo studies in a porcine model. Different heart failure models were used to demonstrate device function across a spectrum of hemodynamic conditions associated with right and left heart failure. These acute in vivo studies demonstrate recovery of blood flow and pressure from the baseline heart failure conditions. Significant reductions in diastolic ventricle pressure were also observed, demonstrating improved filling of the ventricles during diastole, which enables sustainable cardiac output.

Assessing the Collective Dynamics of Motile Cilia in Cultures of Human Airway Cells by Multiscale DDM

The technique of differential dynamic microscopy is extended here, showing that it can provide a powerful and objective method of video analysis for optical microscopy videos of in vitro samples of live human bronchial epithelial ciliated cells. These cells are multiciliated, with motile cilia that play key physiological roles. It is shown that the ciliary beat frequency can be recovered to match conventional analysis, but in a fully automated fashion. Furthermore, it is shown that the properties of spatial and temporal coherence of cilia beat can be recovered and distinguished, and that if a collective traveling wave (the metachronal wave) is present, this has a distinct signature and its wavelength and direction can be measured.

Particle sorting by Paramecium cilia arrays

Motile cilia are cell-surface organelles whose purposes, in ciliated protists and certain ciliated metazoan epithelia, include generating fluid flow, sensing and substance uptake. Certain properties of cilia arrays, such as beating synchronisation and manipulation of external proximate particulate matter, are considered emergent, but remain incompletely characterised despite these phenomena having being the subject of extensive modelling. This study constitutes a laboratory experimental characterisation of one of the emergent properties of motile cilia: manipulation of adjacent particulates. The work demonstrates through automated videomicrographic particle tracking that interactions between microparticles and somatic cilia arrays of the ciliated model organism Paramecium caudatum constitute a form of rudimentary 'sorting'. Small particles are drawn into the organism's proximity by cilia-induced fluid currents at all times, whereas larger particles may be held immobile at a distance from the cell margin when the cell generates characteristic feeding currents in the surrounding media. These findings can contribute to the design and fabrication of biomimetic cilia, with potential applications to the study of ciliopathies.

Hydrodynamic evolution of sperm swimming: Optimal flagella by a genetic algorithm

Swimming performance of spermatozoa is an important index for the success of fertilization. For many years, numerous studies have reported the optimal swimming of flagellar organisms. Nevertheless, there is still a question as to which is optimal among planar, circular helical and ellipsoidal helical beating. In this paper, we use a genetic algorithm to investigate the beat pattern with the best swimming efficiency based on hydrodynamic dissipation and internal torque exertion. For the parameters considered, our results show that the planar beat is optimal for small heads and the helical flagellum is optimum for a larger heads, while the ellipsoidal beat is never optimal. Also, the genetic optimization reveals that the wavenumber and shape of wave envelope are relevant parameters, whereas the wave shape and head geometry have relatively minor effects on efficiency. The optimal beat with respect to the efficiency based on the internal torque exertion of an active elastic flagellum is characterized by a small-wavenumber and large-amplitude wave in a lower-viscosity medium. The obtained results on the optimal waveform are consistent with observations for planar waveforms, but in many respects, the results suggest the necessity of a detailed flagellar structure-fluid interaction to address whether real spermatozoa exhibit hydrodynamically efficient swimming. The evolutional optimization approach used in this study has distinguished biologically important parameters, and the methodology can potentially be applicable to various swimmers.

Anion Effects on the Ion Exchange Process and the Deformation Property of Ionic Polymer Metal Composite Actuators

An ionic polymer-metal composite (IPMC) actuator composed of a thin perfluorinated ionomer membrane with electrodes plated on both surfaces undergoes a large bending motion when a low electric field is applied across its thickness. Such actuators are soft, lightweight, and able to operate in solutions and thus show promise with regard to a wide range of applications, including MEMS sensors, artificial muscles, biomimetic systems, and medical devices. However, the variations induced by changing the type of anion on the device deformation properties are not well understood; therefore, the present study investigated the effects of different anions on the ion exchange process and the deformation behavior of IPMC actuators with palladium electrodes. Ion exchange was carried out in solutions incorporating various anions and the actuator tip displacement in deionized water was subsequently measured while applying a step voltage. In the step voltage response measurements, larger anions such as nitrate or sulfate led to a more pronounced tip displacement compared to that obtained with smaller anions such as hydroxide or chloride. In AC impedance measurements, larger anions generated greater ion conductivity and a larger double-layer capacitance at the cathode. Based on these mechanical and electrochemical measurements, it is concluded that the presence of larger anions in the ion exchange solution induces a greater degree of double-layer capacitance at the cathode and results in enhanced tip deformation of the IPMC actuators.

Hiding the squid: patterns in artificial cephalopod skin

Cephalopods employ their chromomorphic skins for rapid and versatile active camouflage and signalling effects. This is achieved using dense networks of pigmented, muscle-driven chromatophore cells which are neurally stimulated to actuate and affect local skin colouring. This allows cephalopods to adopt numerous dynamic and complex skin patterns, most commonly used to blend into the environment or to communicate with other animals. Our ultimate goal is to create an artificial skin that can mimic such pattern generation techniques, and that could produce a host of novel and compliant devices such as cloaking suits and dynamic illuminated clothing. This paper presents the design, mathematical modelling and analysis of a dynamic biomimetic pattern generation system using bioinspired artificial chromatophores. The artificial skin is made from electroactive dielectric elastomer: a soft, planar-actuating smart material that we show can be effective at mimicking the actuation of biological chromatophores. The proposed system achieves dynamic pattern generation by imposing simple local rules into the artificial chromatophore cells so that they can sense their surroundings in order to manipulate their actuation. By modelling sets of artificial chromatophores in linear arrays of cells, we explore the capability of the system to generate a variety of dynamic pattern types. We show that it is possible to mimic patterning seen in cephalopods, such as the passing cloud display, and other complex dynamic patterning.

How does a flexible chain of active particles swell?

We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First, we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.

Effect of fluid-colloid interactions on the mobility of a thermophoretic microswimmer in non-ideal fluids

Janus colloids propelled by light, e.g., thermophoretic particles, offer promising prospects as artificial microswimmers. However, their swimming behavior and its dependence on fluid properties and fluid-colloid interactions remain poorly understood. Here, we investigate the behavior of a thermophoretic Janus colloid in its own temperature gradient using numerical simulations. The dissipative particle dynamics method with energy conservation is used to investigate the behavior in non-ideal and ideal-gas like fluids for different fluid-colloid interactions, boundary conditions, and temperature-controlling strategies. The fluid-colloid interactions appear to have a strong effect on the colloid behavior, since they directly affect heat exchange between the colloid surface and the fluid. The simulation results show that a reduction of the heat exchange at the fluid-colloid interface leads to an enhancement of colloid's thermophoretic mobility. The colloid behavior is found to be different in non-ideal and ideal fluids, suggesting that fluid compressibility plays a significant role. The flow field around the colloid surface is found to be dominated by a source-dipole, in agreement with the recent theoretical and simulation predictions. Finally, different temperature-control strategies do not appear to have a strong effect on the colloid's swimming velocity.

Swimming efficiency of spherical squirmers: beyond the Lighthill theory

Nonreciprocal shape deformations can drive inertialess cellular swimming, as first explored by Taylor and Lighthill in the 1950s, for the small-amplitude squirming of a planar and a spherical surface, respectively. Lighthill's squirmer, in particular, has been extensively studied for large wave numbers in the context of ciliated microbes. The maximal power efficiency for small-amplitude planar squirming motility is well characterized and degenerate, with nonunique optimal swimming strokes. We explicitly show that this degeneracy is retained at high wave numbers for the small-amplitude spherical squirmer such as a ciliated microbe but is broken for low wave numbers. Hence further complexity emerges in parameter regimes outside that of ciliate swimming even at small amplitudes. Large-amplitude squirming also characterizes more recent observations of large-amplitude/low-wave-number membrane deformations driving the motility of Euglena, neutrophils, and Dictyostelium discoideum. Thus boundary element numerical methods are used to explore swimming with increased deformation amplitudes, especially in the context of power efficiency and swimming performance. As radial squirming amplitudes are increased, small-amplitude linearized theories can be unreliable even for nominally low deformation amplitudes. Furthermore, even for a simple single-mode metachronal wave, a highly motile and efficient large-deformation/small-wave-number swimming modality arises, which can surpass theoretical limitations of purely tangential squirming given a constrained surface deformation velocity.

High-speed holographic microscopy of malaria parasites reveals ambidextrous flagellar waveforms

Axonemes form the core of eukaryotic flagella and cilia, performing tasks ranging from transporting fluid in developing embryos to the propulsion of sperm. Despite their abundance across the eukaryotic domain, the mechanisms that regulate the beating action of axonemes remain unknown. The flagellar waveforms are 3D in general, but current understanding of how axoneme components interact stems from 2D data; comprehensive measurements of flagellar shape are beyond conventional microscopy. Moreover, current flagellar model systems (e.g., sea urchin, human sperm) contain accessory structures that impose mechanical constraints on movement, obscuring the "native" axoneme behavior. We address both problems by developing a high-speed holographic imaging scheme and applying it to the (male) microgametes of malaria (Plasmodium) parasites. These isolated flagella are a unique, mathematically tractable model system for the physics of microswimmers. We reveal the 3D flagellar waveforms of these microorganisms and map the differential shear between microtubules in their axonemes. Furthermore, we overturn claims that chirality in the structure of the axoneme governs the beat pattern [Hirokawa N, et al. (2009) Ann Rev Fluid Mech 41:53-72], because microgametes display a left- or right-handed character on alternate beats. This breaks the link between structural chirality in the axoneme and larger scale symmetry breaking (e.g., in developing embryos), leading us to conclude that accessory structures play a critical role in shaping the flagellar beat.

Emergence of metachronal waves in cilia arrays

Propulsion by cilia is a fascinating and universal mechanism in biological organisms to generate fluid motion on the cellular level. Cilia are hair-like organelles, which are found in many different tissues and many uni- and multicellular organisms. Assembled in large fields, cilia beat neither randomly nor completely synchronously--instead they display a striking self-organization in the form of metachronal waves (MCWs). It was speculated early on that hydrodynamic interactions provide the physical mechanism for the synchronization of cilia motion. Theory and simulations of physical model systems, ranging from arrays of highly simplified actuated particles to a few cilia or cilia chains, support this hypothesis. The main questions are how the individual cilia interact with the flow field generated by their neighbors and synchronize their beats for the metachronal wave to emerge and how the properties of the metachronal wave are determined by the geometrical arrangement of the cilia, like cilia spacing and beat direction. Here, we address these issues by large-scale computer simulations of a mesoscopic model of 2D cilia arrays in a 3D fluid medium. We show that hydrodynamic interactions are indeed sufficient to explain the self-organization of MCWs and study beat patterns, stability, energy expenditure, and transport properties. We find that the MCW can increase propulsion velocity more than 3-fold and efficiency almost 10-fold--compared with cilia all beating in phase. This can be a vital advantage for ciliated organisms and may be interesting to guide biological experiments as well as the design of efficient microfluidic devices and artificial microswimmers.