Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes

The biomolecules of Euglena gracilis: Harnessing biology for natural solutions to future problems

Over the past decade, the autotrophic and heterotrophic protist Euglena gracilis (E. gracilis) has gained popularity across the studies of environmental science, biosynthesis experiments, and nutritional substitutes. The unique physiology and versatile metabolism of E. gracilis have been a recent topic of interest to many researchers who continue to understand the complexity and possibilities of using E. gracilis biomolecule production. In this review, we present a comprehensive representation of recent literature outlining the various uses of biomolecules derived from E. gracilis across the fields of natural product biosynthesis, as a nutritional substitute, and as bioremediation tools. In addition, we highlight effective strategies for altering metabolite production using abiotic stressors and growth conditions. To better understand metabolite biosynthesis and its role in E. gracilis, integrated studies involving genomics, metabolomics, and proteomics should be considered. Together, we show how the ongoing advancements in E. gracilis related research continue to broaden applications in the biosynthetic sector and highlight future works that would strengthen our understanding of overall Euglena metabolism.

Non-Stokesian dynamics of magnetic helical nanoswimmers under confinement

Electromagnetically propelled helical nanoswimmers offer great potential for nanorobotic applications. Here, the effect of confinement on their propulsion is characterized using lattice-Boltzmann simulations. Two principal mechanisms give rise to their forward motion under confinement: (i) pure swimming and (ii) the thrust created by the differential pressure due to confinement. Under strong confinement, they face greater rotational drag but display a faster propulsion for fixed driving frequency in agreement with experimental findings. This is due to the increased differential pressure created by the boundary walls when they are sufficiently close to each other and the particle. We have proposed two analytical relations (i) for predicting the swimming speed of an unconfined particle as a function of its angular speed and geometrical properties, and (ii) an empirical expression to accurately predict the propulsion speed of a confined swimmer as a function of the degree of confinement and its unconfined swimming speed. At low driving frequencies and degrees of confinement, the systems retain the expected linear behavior consistent with the predictions of the Stokes equation. However, as the driving frequency and/or the degree of confinement increase, their impact on propulsion leads to increasing deviations from the Stokesian regime and emergence of nonlinear behavior.

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.

FAP106 is an interaction hub for assembling microtubule inner proteins at the cilium inner junction

Motility of pathogenic protozoa depends on flagella (synonymous with cilia) with axonemes containing nine doublet microtubules (DMTs) and two singlet microtubules. Microtubule inner proteins (MIPs) within DMTs influence axoneme stability and motility and provide lineage-specific adaptations, but individual MIP functions and assembly mechanisms are mostly unknown. Here, we show in the sleeping sickness parasite Trypanosoma brucei, that FAP106, a conserved MIP at the DMT inner junction, is required for trypanosome motility and functions as a critical interaction hub, directing assembly of several conserved and lineage-specific MIPs. We use comparative cryogenic electron tomography (cryoET) and quantitative proteomics to identify MIP candidates. Using RNAi knockdown together with fitting of AlphaFold models into cryoET maps, we demonstrate that one of these candidates, MC8, is a trypanosome-specific MIP required for parasite motility. Our work advances understanding of MIP assembly mechanisms and identifies lineage-specific motility proteins that are attractive targets to consider for therapeutic intervention.

Long-time behavior of swimming Euglena gracilis in a heterogenous light environment

The cell motion of Euglena gracilis in homogeneous and heterogeneous light environments was analyzed. Homogeneous and heterogeneous environments were prepared, with only a red color or with a red circle surrounded by brighter white regions, respectively. In a heterogeneous environment, the cells move into the red circle. Swimming orbits at 1/25 s intervals for 120 s were analyzed. The speed distribution of the 1 s-averaged cell orbits in a homogeneous environment was different from that in a heterogeneous environment, where the faster swimming fraction was enhanced. The relationship between speed and curvature radius was analyzed using a joint histogram. Histograms for short timescale motion, constructed by 1 s-averaged orbits, suggest that the cell swimming curves are not biased, while those for long timescale motion, constructed by 10 s-averaged orbits, suggest that the cell swimming curves are biased in the clockwise direction. Furthermore, the curvature radius determines the speed, which does not seem to depend on the light environment. The mean squared displacement in a heterogeneous environment is larger than that in a homogeneous environment on a 1 s timescale. These results will be the basis for constructing a model for the long-time behavior of photomovement for light differences.

The colloidal nature of complex fluids enhances bacterial motility

The natural habitats of microorganisms in the human microbiome, ocean and soil ecosystems are full of colloids and macromolecules. Such environments exhibit non-Newtonian flow properties, drastically affecting the locomotion of microorganisms^1-5. Although the low-Reynolds-number hydrodynamics of swimming flagellated bacteria in simple Newtonian fluids has been well developed^6-9, our understanding of bacterial motility in complex non-Newtonian fluids is less mature^10,11. Even after six decades of research, fundamental questions about the nature and origin of bacterial motility enhancement in polymer solutions are still under debate^12-23. Here we show that flagellated bacteria in dilute colloidal suspensions display quantitatively similar motile behaviours to those in dilute polymer solutions, in particular a universal particle-size-dependent motility enhancement up to 80% accompanied by a strong suppression of bacterial wobbling^18,24. By virtue of the hard-sphere nature of colloids, whose size and volume fraction we vary across experiments, our results shed light on the long-standing controversy over bacterial motility enhancement in complex fluids and suggest that polymer dynamics may not be essential for capturing the phenomenon^12-23. A physical model that incorporates the colloidal nature of complex fluids quantitatively explains bacterial wobbling dynamics and mobility enhancement in both colloidal and polymeric fluids. Our findings contribute to the understanding of motile behaviours of bacteria in complex fluids, which are relevant for a wide range of microbiological processes²⁵ and for engineering bacterial swimming in complex environments^26,27.

The N -Link Swimmer in Three Dimensions: Controllability and Optimality Results

The controllability of a fully three-dimensional N -link swimmer is studied. After deriving the equations of motion in a low Reynolds number fluid by means of Resistive Force Theory, the controllability of the minimal 2-link swimmer is tackled using techniques from Geometric Control Theory. The shape of the 2-link swimmer is described by two angle parameters. It is shown that the associated vector fields that govern the dynamics generate, via taking their Lie brackets, all eight linearly independent directions in the combined configuration and shape space, leading to controllability; the swimmer can move from any starting configuration and shape to any target configuration and shape by operating on the two shape variables. The result is subsequently extended to the N -link swimmer. Finally, the minimal time optimal control problem and the minimization of the power expended are addressed and a qualitative description of the optimal strategies is provided.

Rotational Locomotion of an Active Gel Driven by Internal Chemical Signals

Chemical waves arising from coupled reaction and transport can serve as biomimetic "nerve signals" to study the underlying origin and regulation of active locomotion. During wave propagation in more than one spatial dimension, the propagation direction of spiral and pulse waves in a nanogel-based PAAm self-oscillating gel, i.e., the orientation of the driving force, may deviate from the normal direction to the wave fronts. Alternating forward and backward retrograde wave locomotion along the normal and tangential kinematic vectors with a phase difference leads to a curved path, i.e., rotational locomotion. This work indicates that appendages in an organism are not required for this type of locomotion. This locomotion mechanism reveals a general principle underlying the dynamical origin of biological helical locomotion and also suggests design approaches for complex locomotion of soft robots and smart materials.

Three-dimensional tracking of the ciliate Tetrahymena reveals the mechanism of ciliary stroke-driven helical swimming

Helical swimming in free-space is a common behavior among microorganisms, such as ciliates that are covered with thousands hair-like motile cilia, and is thought to be essential for cells to orient directly to an external stimulus. However, a direct quantification of their three-dimensional (3D) helical trajectories has not been reported, in part due to difficulty in tracking 3D swimming behavior of ciliates, especially Tetrahymena with a small, transparent cell body. Here, we conducted 3D tracking of fluorescent microbeads within a cell to directly visualize the helical swimming exhibited by Tetrahymena. Our technique showed that Tetrahymena swims along a right-handed helical path with right-handed rolling of its cell body. Using the Tetrahymena cell permeabilized with detergent treatment, we also observed that influx of Ca²⁺ into cilia changed the 3D-trajectory patterns of Tetrahymena swimming, indicating that the beating pattern of cilia is the determining factor in its swimming behavior.

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

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

Structure of the trypanosome paraflagellar rod and insights into non-planar motility of eukaryotic cells

Eukaryotic flagella (synonymous with cilia) rely on a microtubule-based axoneme, together with accessory filaments to carryout motility and signaling functions. While axoneme structures are well characterized, 3D ultrastructure of accessory filaments and their axoneme interface are mostly unknown, presenting a critical gap in understanding structural foundations of eukaryotic flagella. In the flagellum of the protozoan parasite Trypanosoma brucei (T. brucei), the axoneme is accompanied by a paraflagellar rod (PFR) that supports non-planar motility and signaling necessary for disease transmission and pathogenesis. Here, we employed cryogenic electron tomography (cryoET) with sub-tomographic averaging, to obtain structures of the PFR, PFR-axoneme connectors (PACs), and the axonemal central pair complex (CPC). The structures resolve how the 8 nm repeat of the axonemal tubulin dimer interfaces with the 54 nm repeat of the PFR, which consist of proximal, intermediate, and distal zones. In the distal zone, stacked "density scissors" connect with one another to form a "scissors stack network (SSN)" plane oriented 45° to the axoneme axis; and ~370 parallel SSN planes are connected by helix-rich wires into a paracrystalline array with ~90% empty space. Connections from these wires to the intermediate zone, then to overlapping layers of the proximal zone and to the PACs, and ultimately to the CPC, point to a contiguous pathway for signal transmission. Together, our findings provide insights into flagellum-driven, non-planar helical motility of T. brucei and have broad implications ranging from cell motility and tensegrity in biology, to engineering principles in bionics.

Microgel that swims to the beat of light

Complementary to the quickly advancing understanding of the swimming of microorganisms, we demonstrate rather simple design principles for systems that can mimic swimming by body shape deformation. For this purpose, we developed a microswimmer that could be actuated and controlled by fast temperature changes through pulsed infrared light irradiation. The construction of the microswimmer has the following features: (i) it is a bilayer ribbon with a length of 80 or 120 [Formula: see text]m, consisting of a thermo-responsive hydrogel of poly-N-isopropylamide coated with a 2-nm layer of gold and equipped with homogeneously dispersed gold nanorods; (ii) the width of the ribbon is linearly tapered with a wider end of 5 [Formula: see text]m and a tip of 0.5 [Formula: see text]m; (iii) a thickness of only 1 and 2 [Formula: see text]m that ensures a maximum variation of the cross section of the ribbon along its length from square to rectangular. These wedge-shaped ribbons form conical helices when the hydrogel is swollen in cold water and extend to a filament-like object when the temperature is raised above the volume phase transition of the hydrogel at [Formula: see text]. The two ends of these ribbons undergo different but coupled modes of motion upon fast temperature cycling through plasmonic heating of the gel-objects from inside. Proper choice of the IR-light pulse sequence caused the ribbons to move at a rate of 6 body length/s (500 [Formula: see text]m/s) with the wider end ahead. Within the confinement of rectangular container of 30 [Formula: see text]m height and 300 [Formula: see text]m width, the different modes can be actuated in a way that the movement is directed by the energy input between spinning on the spot and fast forward locomotion.

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.

A new kind of beat

New mathematical model reveals how the flagella of some single-celled algae generate a lasso-like beat pattern that propels the cell through water.

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.

Helical Klinotactic Locomotion of Two-Link Nanoswimmers with Dual-Function Drug-Loaded Soft Polysaccharide Hinges

Inspired by the movement of bacteria and other microorganisms, researchers have developed artificial helical micro- and nanorobots that can perform corkscrew locomotion or helical path swimming under external energy actuation. In this paper, for the first time the locomotion of nonhelical multifunctional nanorobots that can swim in helical klinotactic trajectories, similarly to rod-shaped bacteria, under rotating magnetic fields is investigated. These nanorobots consist of a rigid ferromagnetic nickel head connected to a rhodium tail by a flexible hydrogel-based hollow hinge composed of chemically responsive chitosan and alginate multilayers. This design allows nanoswimmers switching between different dynamic behaviors-from in-plane tumbling to helical klinotactic swimming-by varying the rotating magnetic field frequency and strength. It also adds a rich spectrum of swimming capabilities that can be adjusted by varying the type of applied magnetic fields and/or frequencies. A theoretical model is developed to analyze the propulsion mechanisms and predict the swimming behavior at distinct rotating magnetic frequencies. The model shows good agreement with the experimental results. Additionally, the biomedical capabilities of the nanoswimmers as drug delivery platforms are demonstrated. Unlike previous designs constitute metallic segments, the proposed nanoswimmers can encapsulate drugs into their hollow hinge and successfully release them to cells.

How Euglena gracilis swims: Flow field reconstruction and analysis

Euglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke. We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching. Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.

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.

Controlling Cell Motion and Microscale Flow with Polarized Light Fields

We investigate how light polarization affects the motion of photoresponsive algae, Euglena gracilis. In a uniformly polarized field, cells swim approximately perpendicular to the polarization direction and form a nematic state with zero mean velocity. When light polarization varies spatially, cell motion is modulated by local polarization. In such light fields, cells exhibit complex spatial distribution and motion patterns which are controlled by topological properties of the underlying fields; we further show that ordered cell swimming can generate directed transporting fluid flow. Experimental results are quantitatively reproduced by an active Brownian particle model in which particle motion direction is nematically coupled to local light polarization.

Flagellum Malfunctions Trigger Metaboly as an Escape Strategy in Euglena gracilis

Euglenoids present the ability to alter the shape of their bodies, a process referred to as metaboly. Metaboly is usually used by phagotrophic cells to engulf their prey. However, Euglena gracilis is osmotrophic and photosynthetic. Though metaboly was discovered centuries ago, it remains unclear why E. gracilis undergo metaboly and what causes them to deform, and some consider metaboly to be a functionless ancestral vestige. Here, we discover that flagellum malfunctions trigger metaboly and metaboly is a smart escape strategy adopted by E. gracilis when the proper rotation and beating of the flagellum are hindered by restrictions including surface obstruction, sticking, resistance, or limited space. Metaboly facilitates escape in five ways: (i) detaching the body from the surface; (ii) enlarging the space between flagellum and the restricting surface which restores beating and rotation of the flagellum; (iii) decreasing the torque of viscous resistance for rotation of the body; (iv) decreasing the length of the body; and (v) crawling backwards on a surface or swimming backwards if the flagellum completely malfunctions or has broken off. Our findings suggest that metaboly plays a key role in enabling E. gracilis to escape from harmful conditions when flagellar functions are impaired or absent.

Flagellar kinematics reveals the role of environment in shaping sperm motility

Swimming spermatozoa from diverse organisms often have very similar morphologies, yet different motilities as a result of differences in the flagellar waveforms used for propulsion. The origin of these differences has remained largely unknown. Using high-speed video microscopy and mathematical analysis of flagellar shape dynamics, we quantitatively compare sperm flagellar waveforms from marine invertebrates to humans by means of a novel phylokinematic tree. This new approach revealed that genetically dissimilar sperm can exhibit strikingly similar flagellar waveforms and identifies two dominant flagellar waveforms among the deuterostomes studied here, corresponding to internal and external fertilizers. The phylokinematic tree shows marked discordance from the phylogenetic tree, indicating that physical properties of the fluid environment, more than genetic relatedness, act as an important selective pressure in shaping the evolution of sperm motility. More broadly, this work provides a physical axis to complement morphological and genetic studies to understand evolutionary relationships.

Active Reversible Swimming of Magnetically Assembled "Microscallops" in Non-Newtonian Fluids

Miniaturized devices capable of active swimming at low Reynolds numbers are of fundamental importance and possess potential biomedical utility. The design of colloidal microswimmers requires not only miniaturizing reconfigurable structures but also understanding their interactions with media at low Reynolds numbers. We investigate the dynamics of "microscallops" made of asymmetric magnetic cubes, which are assembled and actuated using magnetic fields. One approach to achieving directional propulsion is to break the symmetry of the viscous forces by coupling the reciprocal motions of such microswimmers with the nonlinear rheology inherent in non-Newtonian fluids. When placed in shear-thinning fluids, the local viscosity gradient resulting from nonuniform shear stresses exerted by time-asymmetric strokes of the microscallops generates propulsive thrust through an effect we term "self-viscophoresis". Surprisingly, we found that the direction of propulsion changes with the size and structure of these assemblies. We analyze the origins of their directional propulsion and explain the variable propulsion direction in terms of multiple counterbalancing domains of shear dissipation around the microscale structures. The principles governing the locomotion of these microswimmers may be extended to other reconfigurable microbots assembled from colloidal-scale units.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Growth and remodelling of living tissues: perspectives, challenges and opportunities

One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.

Swimming Euglena respond to confinement with a behavioral change enabling effective crawling

Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large amplitude peristaltic body deformations. This remarkable behavior has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behavior is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modeling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells.

Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions

Interest in the design of bioinspired robotic microswimmers is growing rapidly, motivated by the spectacular capabilities of their unicellular biological templates. Predicting the swimming speed and efficiency of such devices in a reliable way is essential for their rational design, and to optimize their performance. The hydrodynamic simulations needed for this purpose are demanding and simplified models that neglect nonlocal hydrodynamic interactions (e.g., resistive force theory for slender, filament-like objects that are the typical propulsive apparatus for unicellular swimmers) are commonly used. We show through a detailed case study of a model robotic system consisting of a spherical head powered by a rotating helical flagellum that (a) the errors one makes in the prediction of swimming speed and efficiency by neglecting hydrodynamic interactions are never quite acceptable and (b) there are simple ways to correct the predictions of the simplified theories to make them more accurate. We also formulate optimal design problems for the length of the helical flagellum giving maximal energetic efficiency, maximal distance traveled per motor turn, or maximal distance traveled per unit of work expended, and exhibit optimal solutions.

Autophoretic motion in three dimensions

Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. Their motion typically consists of straight paths with rotational diffusion being the dominant reorientation mechanism. In this paper, we show theoretically that by a suitable surface coverage of both activity and mobility, translational and rotational motion can be induced arbitrarily in three dimensions. The resulting trajectories are in general helical, and their pitch and radius can be controlled by adjusting the angle between the translational and angular velocity. Building on the classical mathematical framework for axisymmetric self-phoretic motion under fixed-flux chemical boundary conditions, we first show how to calculate the most general three-dimensional motion for an arbitrary surface coverage of a spherical particle. After illustrating our results on surface distributions, we next introduce a simple intuitive patch model to serve as a guide for designing arbitrary phoretic spheres.