Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes

Inertia and activity: spiral transitions in semi-flexible, self-avoiding polymers

We consider a two-dimensional, tangentially active, semi-flexible, self-avoiding polymer to find a dynamical re-entrant transition between motile open chains and spinning achiral spirals with increasing activity. Utilizing probability distributions of the turning number, we ascertain the comparative stability of the spiral structure and present a detailed phase diagram within the activity inertia plane. The onset of spiral formation at low activity levels is governed by a torque balance and is independent of inertia. At higher activities, however, inertial effects lead to spiral destabilization, an effect absent in the overdamped limit. We further delineate alterations in size and shape by analyzing the end-to-end distance distribution and the radius of gyration tensor. The Kullback-Leibler divergence from equilibrium distributions exhibits a non-monotonic relationship with activity, reaching a peak at the most compact spirals characterized by the most persistent spinning. As inertia increases, this divergence from equilibrium diminishes.

Local elasticity evaluation of acid-denatured collagen by photoacoustic spectroscopy

While there are various analytical methods for elasticity evaluation, those with micrometer-order spatial resolution are still under developing. As some of biological tissues such as capillary vessels and cochlea are very small and/or highly heterogeneous, development of analytical techniques with such high spatial resolution has been desired for biological and medical purposes. Especially, the elasticity of capillary vessels (several micrometer in diameter) would be an important indicator to find out early diseases. To measure the local elasticity for such small and/or heterogeneous samples, we have proposed an approach based on a temporal waveform of photoacoustic (PA) signal, i.e., time-domain PA. As the time-domain PA contains both the vibrating frequency and the sound propagation time after the excitation, it provides the information on the local elasticity (from the frequency) at a specific depth (from the propagation time) of samples. In the present study, the signal from collagen sheets were obtained and analyzed as models of blood vessel walls and scaffolds for regenerative medicine. In contrast to previous studies using the agarose gel which showed a single frequency peak, the signal from the collagen sheets was mainly composed of two frequency peaks, assignable to surface and bulk vibration. Further, the bulk vibration was found to sensitively reflect the elasticity of the samples. Since the PA effect can be induced only at the position where the light absorber exists, the analytical method proposed here would allow us to measure the local elasticity and its spatial distribution in blood vessels and other tissues.

Large Scale Zigzag Pattern Emerging from Circulating Active Shakers

We report the emergence of large zigzag bands in a population of reversibly actuated magnetic rotors that behave as active shakers, namely squirmers that shake the fluid around them without moving. The shakers collectively organize into dynamic structures displaying self-similar growth and generate topological defects in the form of cusps that connect vortices of rolling particles with alternating chirality. By combining experimental analysis with particle-based simulation, we show that the special flow field created by the shakers is the only ingredient needed to reproduce the observed spatiotemporal pattern. We unveil a self-organization scenario in a collection of driven particles in a viscoelastic medium emerging from the reduced particle degrees of freedom, as here the frozen orientational motion of the shakers.

Helical Locomotion in Yield Stress Fluids

We report three stages for locomotion of a helical swimmer in yield stress fluids. In the first stage, the swimmer must overcome the material's yield strain to generate rotational motion. However, exceeding the first threshold is not sufficient for locomotion. Only when the viscous forces are sufficiently strong to plastically deform the material to a finite distance away from the swimmer will net locomotion occur. Once locomotion is underway in the third stage, the yield stress retards swimming at small pitch angles. Conversely, at large pitch angles, yield stress dominates the flow by enhancing swimming speed. Flow visualizations reveal a highly localized flow near the swimmer in yield stress fluids.

Facilitated dynamics of an active polymer in 2D crowded environments with obstacles

Understanding the behaviors of a single active chain in complex environments is not only an interesting topic in non-equilibrium physics but also has applicative implications in biological/medical engineering. In this work, by using molecular simulations, we systematically study the dynamical and conformational behaviors of an active polymer in crowded environments, i.e., a single active chain confined in 2D space with randomly arranged obstacles. We found that the competition between the chain's activity and rigidity in the presence of obstacles leads to many interesting dynamical and conformational states, such as the diffusive expanded state, the diffusive collapsed state, and the localized collapsed state. Importantly, we found a counter-intuitive phenomenon, i.e., crowded environments facilitate the diffusion of the active polymer within a large parameter space. As the crowdedness (packing fraction of obstacles) increases, the parameter space in which crowding-enhanced diffusion occurs still remains. This abnormal dynamics is attributed to a structural reason that the obstacles prevent active chains from collapsing. Our findings capture some generic features of active polymers in complex environments and provide insights into the design of novel drug delivery systems.

Understanding enhanced rotational dynamics of active probes in rod suspensions

Active Brownian particles (APs) have recently been shown to exhibit enhanced rotational diffusion (ERD) in complex fluids. Here, we experimentally observe ERD and numerically corroborate its microscopic origin for a quasi-two-dimensional suspension of colloidal rods. At high density, the rods form small rafts, wherein they perform small-amplitude, high-frequency longitudinal displacements. Activity couples AP-rod contacts to reorientation, with the variance therein leading to ERD. This is captured by a local, rather than a global relaxation time, as used in previous phenomenological modeling. Our result should prove relevant to the microrheological characterization of complex fluids and furthering our understanding of the dynamics of microorganisms in such media.

Performance of a Helical Microswimmer Traversing a Discrete Viscoelastic Network with Dynamic Remodeling

Microorganisms often navigate a complex environment composed of a viscous fluid with suspended microstructures such as elastic polymers and filamentous networks. These microstructures can have similar length scales to the microorganisms, leading to complex swimming dynamics. Some microorganisms secrete enzymes that dynamically change the elastic properties of the viscoelastic networks through which they move. In addition to biological organisms, microrobots have been engineered with the goals of mucin gel penetration or dissolving blood clots. In order to gain insight into the coupling between swimming performance and network remodeling, we used a regularized Stokeslet boundary element method to compute the motion of a microswimmer consisting of a rotating spherical body and counter-rotating helical flagellum. The viscoelastic network is represented by a network of points connected by virtual elastic linkages immersed in a viscous fluid. Here, we model the enzymatic dissolution of the network by bacteria or microrobots by dynamically breaking elastic linkages when the cell body of the swimmer falls within a given distance from the link. We investigate the swimming performance of the microbes as they penetrate and move through networks of different material properties, and also examine the effect of network remodeling.

Spinning-enabled wireless amphibious origami millirobot

Wireless millimeter-scale origami robots have recently been explored with great potential for biomedical applications. Existing millimeter-scale origami devices usually require separate geometrical components for locomotion and functions. Additionally, none of them can achieve both on-ground and in-water locomotion. Here we report a magnetically actuated amphibious origami millirobot that integrates capabilities of spinning-enabled multimodal locomotion, delivery of liquid medicine, and cargo transportation with wireless operation. This millirobot takes full advantage of the geometrical features and folding/unfolding capability of Kresling origami, a triangulated hollow cylinder, to fulfill multifunction: its geometrical features are exploited for generating omnidirectional locomotion in various working environments through rolling, flipping, and spinning-induced propulsion; the folding/unfolding is utilized as a pumping mechanism for controlled delivery of liquid medicine; furthermore, the spinning motion provides a sucking mechanism for targeted solid cargo transportation. We anticipate the amphibious origami millirobots can potentially serve as minimally invasive devices for biomedical diagnoses and treatments.

Wireless millirobots are promising as minimally invasive biomedical devices. Here, the authors design a magnetically actuated amphibious millirobot that integrates spinning-enabled locomotion, targeted drug delivery, and cargo transportation by utilizing geometrical features and folding/unfolding capability of the Kresling origami.

Orbital magnetism of an active particle in viscoelastic suspension

We consider an active (self-propelling) particle in a viscoelastic fluid. The particle is charged and constrained to move in a two-dimensional harmonic trap. Its dynamics is coupled to a constant magnetic field applied perpendicular to its plane of motion via Lorentz force. Due to the finite activity, the generalized fluctuation-dissipation relation (GFDR) breaks down, driving the system away from equilibrium. While breaking GFDR, we have shown that the system can have finite classical orbital magnetism only when the dynamics of the system contains finite inertia. The orbital magnetic moment has been calculated exactly. Remarkably, we find that when the elastic dissipation timescale of the medium is larger (smaller) than the persistence timescale of the self-propelling particle, it is diamagnetic (paramagnetic). Therefore, for a given strength of the magnetic field, the system undergoes a transition from diamagnetic to paramagnetic state (and vice versa) simply by tuning the timescales of underlying physical processes, such as active fluctuations and viscoelastic dissipation. Interestingly, we also find that the magnetic moment, which vanishes at equilibrium, behaves nonmonotonically with respect to increasing persistence of self-propulsion, which drives the system out of equilibrium.

Rolling controls sperm navigation in response to the dynamic rheological properties of the environment

Mammalian sperm rolling around their longitudinal axes is a long-observed component of motility, but its function in the fertilization process, and more specifically in sperm migration within the female reproductive tract, remains elusive. While investigating bovine sperm motion under simple shear flow and in a quiescent microfluidic reservoir and developing theoretical and computational models, we found that rolling regulates sperm navigation in response to the rheological properties of the sperm environment. In other words, rolling enables a sperm to swim progressively even if the flagellum beats asymmetrically. Therefore, a rolling sperm swims stably along the nearby walls (wall-dependent navigation) and efficiently upstream under an external fluid flow (rheotaxis). By contrast, an increase in ambient viscosity and viscoelasticity suppresses rolling, consequently, non-rolling sperm are less susceptible to nearby walls and external fluid flow and swim in two-dimensional diffusive circular paths (surface exploration). This surface exploration mode of swimming is caused by the intrinsic asymmetry in flagellar beating such that the curvature of a sperm's circular path is proportional to the level of asymmetry. We found that the suppression of rolling is reversible and occurs in sperm with lower asymmetry in their beating pattern at higher ambient viscosity and viscoelasticity. Consequently, the rolling component of motility may function as a regulatory tool allowing sperm to navigate according to the rheological properties of the functional region within the female reproductive tract.

Mapping Viscoelastic Properties Using Helical Magnetic Nanopropellers

Artificial micro/nanomachines have been envisioned and demonstrated as potential candidates for targeted drug or gene delivery, cell manipulation, environmental and biological sensing and in lab on chip applications. Here, we have used helical nanomachines to measure the local rheological properties of a viscoelastic media. The position of the helical nanomachine/ nanopropeller was controlled precisely using magnetic fields with simultaneous measurements of the mechanical properties of a complex and heterogeneous fluidic environment. We demonstrated that the motion of the helical nanopropeller is extremely sensitive to fluid elasticity and the speed of propulsion of the nanopropeller can be used as a measure of the local elastic relaxation time. Taken together, we report a promising new technique of mapping the rheological properties by helical nanopropellers with very high spatial and temporal resolutions, with performance superior to existing techniques of passive or active microrheology.

Co-Adaptation of Physical Attributes of the Mammalian Female Reproductive Tract and Sperm to Facilitate Fertilization

The functions of the female reproductive tract not only encompass sperm migration, storage, and fertilization, but also support the transport and development of the fertilized egg through to the birth of offspring. Further, because the tract is open to the external environment, it must also provide protection against invasive pathogens. In biophysics, sperm are considered “pusher microswimmers”, because they are propelled by pushing fluid behind them. This type of swimming by motile microorganisms promotes the tendency to swim along walls and upstream in gentle fluid flows. Thus, the architecture of the walls of the female tract, and the gentle flows created by cilia, can guide sperm migration. The viscoelasticity of the fluids in the tract, such as mucus secretions, also promotes the cooperative swimming of sperm that can improve fertilization success; at the same time, the mucus can also impede the invasion of pathogens. This review is focused on how the mammalian female reproductive tract and sperm interact physically to facilitate the movement of sperm to the site of fertilization. Knowledge of female/sperm interactions can not only explain how the female tract can physically guide sperm to the fertilization site, but can also be applied for the improvement of in vitro fertilization devices.

Helical locomotion in a porous medium

Microorganisms and artificial microswimmers often need to swim through environments that are more complex than purely viscous liquids in their natural habitats or operational environments, such as gel-like mucus, wet soil, and aquifers. The question of how the properties of these complex environments affect locomotion has attracted considerable recent attention. In this paper, we present a theoretical model to examine how the additional resistance due to the network of stationary obstacles in a porous medium affects helical locomotion. Here, we focus on helical locomotion for its ubiquity as a propulsion mechanism adopted by many swimming bacteria and artificial microswimmers. We show that the additional resistance can have qualitatively different effects on various scenarios of helical locomotion: (1) a helical propeller driven by an external torque, (2) a free swimming bacterium consisting of a helical flagellum and a head, and (3) a cargo-carrying helical propeller driven by an external torque. Our results elucidate the subtle and significant differences between torqued helical propulsion versus force-free and torque-free swimming in a porous medium. We also remark on the limitations as well as potential connections of our results with experimental measurements of bacterial swimming speeds in polymeric solutions.

Fantastic Voyage of Nanomotors into the Cell

Richard Feynman's 1959 vision of controlling devices at small scales and swallowing the surgeon has inspired the science-fiction Fantastic Voyage film and has played a crucial role in the rapid development of the microrobotics field. Sixty years later, we are currently witnessing a dramatic progress in this field, with artificial micro- and nanoscale robots moving within confined spaces, down to the cellular level, and performing a wide range of biomedical applications within the cellular interior while addressing the limitations of common passive nanosystems. In this review article, we discuss key recent advances in the field of micro/nanomotors toward important cellular applications. Specifically, we outline the distinct capabilities of nanoscale motors for such cellular applications and illustrate how the active movement of nanomotors leads to distinct advantages of rapid cell penetration, accelerated intracellular sensing, and effective intracellular delivery toward enhanced therapeutic efficiencies. We finalize by discussing the future prospects and key challenges that such micromotor technology face toward implementing practical intracellular applications. By increasing our knowledge of nanomotors' cell entry and of their behavior within the intracellular space, and by successfully addressing key challenges, we expect that next-generation nanomotors will lead to exciting advances toward cell-based diagnostics and therapy.

Medical micro/nanorobots in complex media

Medical micro/nanorobots have received tremendous attention over the past decades owing to their potential to be navigated into hard-to-reach tissues for a number of biomedical applications ranging from targeted drug/gene delivery, bio-isolation, detoxification, to nanosurgery. Despite the great promise, the majority of the past demonstrations are primarily under benchtop or in vitro conditions. Many developed micro/nanoscale propulsion mechanisms are based on the assumption of a homogeneous, Newtonian environment, while realistic biological environments are substantially more complex. Moving toward practical medical use, the field of micro/nanorobotics must overcome several major challenges including propulsion through complex media (such as blood, mucus, and vitreous) as well as deep tissue imaging and control in vivo. In this review article, we summarize the recent research efforts on investigating how various complexities in biological environments impact the propulsion of micro/nanoswimmers. We also highlight the emerging technological approaches to enhance the locomotion of micro/nanorobots in complex environments. The recent demonstrations of in vivo imaging, control and therapeutic medical applications of such micro/nanorobots are introduced. We envision that continuing materials and technological innovations through interdisciplinary collaborative efforts can bring us steps closer to the fantasy of "swallowing a surgeon".

Helical nanobots as mechanical probes of intra- and extracellular environments

A rheological probe that can measure mechanical properties of biological milieu at well-defined locations with high spatial resolution, on a time scale faster than most biological processes, can further improve our understanding of how living systems operate and behave. Here, we demonstrate nanorobots actively driven in realistic ex vivo biological systems for fast mechanical measurements with high spatial accuracy. In the various demonstrations of magnetic nanobots as mechanical probes, we report the first direct observation of the internalization of probes by a living cell, the accurate measurement of the 'fluid phase' cytoplasmic viscosity of ~200 cP for a HeLa cell, demonstration of intracellular measurements in cells derived from human patients; all of which establish the strength of this novel technique for measurements in both intra- and extracellular environments.

Enhanced Rotational Motion of Spherical Squirmer in Polymer Solutions

The rotational diffusive motion of a self-propelled, attractive spherical colloid immersed in a solution of self-avoiding polymers is studied by mesoscale hydrodynamic simulations. A drastic enhancement of the rotational diffusion by more than an order of magnitude in the presence of activity is obtained. The amplification is a consequence of two effects, a decrease of the amount of adsorbed polymers by active motion and an asymmetric encounter with polymers on the squirmer surface, which yields an additional torque and random noise for the rotational motion. Our simulations suggest a way to control the rotational dynamics of squirmer-type microswimmers by the degree of polymer adsorption and system heterogeneity.

Dynamics of Active Filaments in Porous Media

The motion of active polymers in a two-dimensional porous medium is shown to depend critically on flexibility, activity, and degree of polymerization. For a given Péclet number, we observe a transition from localization to diffusion as the stiffness of the chains is increased. Whereas stiff chains move almost unhindered through the porous medium, flexible ones spiral and get stuck. Their motion can be accounted for by the model of a continuous time random walk with a renewal process corresponding to unspiraling. The waiting time distribution is shown to develop heavy tails for decreasing stiffness, resulting in subdiffusive and ultimately caged behavior.

Mechanical shear controls bacterial penetration in mucus

Mucus plays crucial roles in higher organisms, from aiding fertilization to protecting the female reproductive tract. Here, we investigate how anisotropic organization of mucus affects bacterial motility. We demonstrate by cryo electron micrographs and elongated tracer particles imaging, that mucus anisotropy and heterogeneity depend on how mechanical stress is applied. In shallow mucus films, we observe bacteria reversing their swimming direction without U-turns. During the forward motion, bacteria burrowed tunnels that last for several seconds and enable them to swim back faster, following the same track. We elucidate the physical mechanism of direction reversal by fluorescent visualization of the flagella: when the bacterial body is suddenly stopped by the mucus structure, the compression on the flagellar bundle causes buckling, disassembly and reorganization on the other side of the bacterium. Our results shed light into motility of bacteria in complex visco-elastic fluids and can provide clues in the propagation of bacteria-born diseases in mucus.

Three-dimensional simulations of undulatory and amoeboid swimmers in viscoelastic fluids

Microorganisms often move through viscoelastic environments, as biological fluids frequently have a rich microstructure owing to the presence of large polymeric molecules. Research on the effect of fluid elasticity on the swimming kinematics of these organisms has usually been focused on those that move via cilia or flagellum. Experimentally, Shen (X. N. Shen et al., Phys. Rev. Lett., 2011, 106, 208101) reported that the nematode C. elegans, a model organism used to study undulatory motion, swims more slowly as the Deborah number describing the fluid's elasticity is increased. This phenomenon has not been thoroughly studied via a fully resolved three-dimensional simulation; moreover, the effect of fluid elasticity on the swimming speed of organisms moving via euglenoid movement, such as E. gracilis, is completely unknown. In this study, we discuss the simulation of the arbitrary motion of an undulating or pulsating swimmer that occupies finite volume in three dimensions, with the ability to specify any differential viscoelastic rheological model for the surrounding fluid. To accomplish this task, we use a modified version of the Immersed Finite Element Method presented in a previous paper by Guido and Saadat in 2018 (A. Saadat et al., Phys. Rev. E, 2018, 98, 063316). In particular, this version allows for the simulation of deformable swimmers such that they evolve through an arbitrary set of specified shapes via a conformation-driven force. From our analysis, we observe several key trends not found in previous two-dimensional simulations or theoretical analyses for C. elegans, as well as novel results for the amoeboid motion. In particular, we find that regions of high polymer stress concentrated at the head and tail of the swimming C. elegans are created by strong extensional flow fields and are associated with a decrease in swimming speed for a given swimming stroke. In contrast, in two dimensions these regions of stress are commonly found distributed along the entire body, likely owing to the lack of a third dimension for polymer relaxation. A comparison of swim speeds shows that the calculations in two-dimensional simulations result in an over-prediction of the speed reduction. We believe that our simulation tool accurately captures the swimming motion of the two aforementioned model swimmers and furthermore, allows for the simulation of multiple deformable swimmers, as well as more complex swimming geometries. This methodology opens many new possibilities for future studies of swimmers in viscoelastic fluids.

A Review of Micromotors in Confinements: Pores, Channels, Grooves, Steps, Interfaces, Chains, and Swimming in the Bulk

One of the recent frontiers of nanotechnology research involves machines that operate at nano- and microscales, also known as nano/micromotors. Their potential applications in biomedicine, environmental sciences and engineering, military and defense industries, self-assembly, and many other areas have fueled an intense interest in this topic over the last 15 years. Despite deepened understanding of their propulsion mechanisms, we are still in the early days of exploring the dynamics of micromotors in complex and more realistic environments. Confinements, as a typical example of complex environments, are extremely relevant to the applications of micromotors, which are expected to travel in mucus gels, blood vessels, reproductive and digestive tracts, microfluidic chips, and capillary tubes. In this review, we summarize and critically examine recent studies (mostly experimental ones) of micromotor dynamics in confinements in 3D (spheres and porous network, channels, grooves, steps, and obstacles), 2D (liquid-liquid, liquid-solid, and liquid-air interfaces), and 1D (chains). In addition, studies of micromotors moving in the bulk solution and the usefulness of acoustic levitation is discussed. At the end of this article, we summarize how confinements can affect micromotors and offer our insights on future research directions. This review article is relevant to readers who are interested in the interactions of materials with interfaces and structures at the microscale and helpful for the design of smart and multifunctional materials for various applications.

Enhanced locomotion, effective diffusion and trapping of undulatory micro-swimmers in heterogeneous environments

Swimming cells and microorganisms must often move through complex fluids that contain an immersed microstructure such as polymer molecules or filaments. In many important biological processes, such as mammalian reproduction and bacterial infection, the size of the immersed microstructure is comparable to that of the swimming cells. This leads to discrete swimmer-microstructure interactions that alter the swimmer's path and speed. In this paper, we use a combination of detailed simulation and data-driven stochastic models to examine the motion of a planar undulatory swimmer in an environment of spherical obstacles tethered via linear springs to random points in the plane of locomotion. We find that, depending on environmental parameters, the interactions with the obstacles can enhance swimming speeds or prevent the swimmer from moving at all. We also show how the discrete interactions produce translational and angular velocity fluctuations that over time lead to diffusive behaviour primarily due to the coupling of swimming and rotational diffusion. Our results demonstrate that direct swimmer-microstructure interactions can produce changes in swimmer motion that may have important implications for the spreading of cell populations in or the trapping of harmful pathogens by complex fluids.

Maneuverability of Magnetic Nanomotors Inside Living Cells

Spatiotemporally controlled active manipulation of external micro-/nanoprobes inside living cells can lead to development of innovative biomedical technologies and inspire fundamental studies of various biophysical phenomena. Examples include gene silencing applications, real-time mechanical mapping of the intracellular environment, studying cellular response to local stress, and many more. Here, for the first time, cellular internalization and subsequent intracellular manipulation of a system of helical nanomotors driven by small rotating magnetic fields with no adverse effect on the cellular viability are demonstrated. This remote method of fuelling and guidance limits the effect of mechanical transduction to cells containing external probes, in contrast to ultrasonically or chemically powered techniques that perturb the entire experimental volume. The investigation comprises three cell types, containing both cancerous and noncancerous types, and is aimed toward analyzing and engineering the motion of helical propellers through the crowded intracellular space. The studies provide evidence for the strong anisotropy, heterogeneity, and spatiotemporal variability of the cellular interior, and confirm the suitability of helical magnetic nanoprobes as a promising tool for future cellular investigations and applications.

Changes in the flagellar bundling time account for variations in swimming behavior of flagellated bacteria in viscous media

Although the motility of the flagellated bacteria, Escherichia coli, has been widely studied, the effect of viscosity on swimming speed remains controversial. The swimming mode of wild-type E. coli is often idealized as a run-and-tumble sequence in which periods of swimming at a constant speed are randomly interrupted by a sudden change of direction at a very low speed. Using a tracking microscope, we follow cells for extended periods of time in Newtonian liquids of varying viscosity and find that the swimming behavior of a single cell can exhibit a variety of behaviors, including run and tumble and "slow random walk" in which the cells move at a relatively low speed. Although the characteristic swimming speed varies between individuals and in different polymer solutions, we find that the skewness of the speed distribution is solely a function of viscosity and can be used, in concert with the measured average swimming speed, to determine the effective running speed of each cell. We hypothesize that differences in the swimming behavior observed in solutions of different viscosity are due to changes in the flagellar bundling time, which increases as the viscosity rises, due to the lower rotation rate of the flagellar motor. A numerical simulation and the use of resistive force theory provide support for this hypothesis.

Flagellar swimming in viscoelastic fluids: role of fluid elastic stress revealed by simulations based on experimental data

Many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus and wet soil. The effects of fluid elasticity on motility remain poorly understood, partly because the swimmer strokes depend on the properties of the fluid medium, which obfuscates the mechanisms responsible for observed behavioural changes. In this study, we use experimental data on the gaits of Chlamydomonas reinhardtii swimming in Newtonian and viscoelastic fluids as inputs to numerical simulations that decouple the swimmer gait and fluid type in order to isolate the effect of fluid elasticity on swimming. In viscoelastic fluids, cells employing the Newtonian gait swim faster but generate larger stresses and use more power, and as a result the viscoelastic gait is more efficient. Furthermore, we show that fundamental principles of swimming based on viscous fluid theory miss important flow dynamics: fluid elasticity provides an elastic memory effect that increases both the forward and backward speeds, and (unlike purely viscous fluids) larger fluid stress accumulates around flagella moving tangent to the swimming direction, compared with the normal direction.

Passive and Active Microrheology of the Intestinal Fluid of the Larval Zebrafish

The fluids of the intestine serve as a physical barrier to pathogens, a medium for the diffusion of nutrients and metabolites, and an environment for commensal microbes. The rheological properties of intestinal mucus have therefore been the subject of many investigations, thus far limited to in vitro studies due to the difficulty of measurement in the natural context of the gut. This limitation especially hinders our understanding of how the gut microbiota interact with the intestinal space, since examination of this calls not only for in vivo measurement techniques, but for techniques that can be applied to model organisms in which the microbial state of the gut can be controlled. We have addressed this challenge with two complementary approaches. We performed passive microrheological measurements using thermally driven nanoparticles and active microrheology using micron-scale ellipsoidal magnetic microparticles, in both cases using light-sheet fluorescence microscopy to optically access the intestinal bulb of the larval zebrafish, a model vertebrate. We present viscosity measurements in germ-free animals (devoid of gut microbes), animals colonized by a single bacterial species, and conventionally reared animals, and find that in all cases, the mucin-rich intestinal liquid is well described as a Newtonian fluid. Surprisingly, despite known differences in the number of secretory cells in germ-free zebrafish and their conventional counterparts, the fluid viscosity for these two groups is very similar, as measured with either technique. Our study provides, to our knowledge, the first in vivo microrheological measurements of the intestinal space in living animals, and we comment on its implications for timescales of host-microbe interactions in the gut.

Helical Locomotion in a Granular Medium

The physical mechanisms that bring about the propulsion of a rotating helix in a granular medium are considered. A propulsive motion along the axis of the rotating helix is induced by both symmetry breaking due to the helical shape, and the anisotropic frictional forces undergone by all segments of the helix in the medium. Helix dynamics is studied as a function of helix rotation speed and its geometrical parameters. The effect of the granular pressure and the applied external load were also investigated. A theoretical model is developed based on the anisotropic frictional force experienced by a slender body moving in a granular material, to account for the translation speed of the helix. A good agreement with experimental data is obtained, which allows for predicting the helix design to propel optimally within granular media. These results pave the way for the development of an efficient sand robot operating according to this mode of locomotion.

Fluid viscoelasticity promotes collective swimming of sperm

From flocking birds to swarming insects, interactions of organisms large and small lead to the emergence of collective dynamics. Here, we report striking collective swimming of bovine sperm in dynamic clusters, enabled by the viscoelasticity of the fluid. Sperm oriented in the same direction within each cluster, and cluster size and cell-cell alignment strength increased with viscoelasticity of the fluid. In contrast, sperm swam randomly and individually in Newtonian (nonelastic) fluids of low and high viscosity. Analysis of the fluid motion surrounding individual swimming sperm indicated that sperm-fluid interaction was facilitated by the elastic component of the fluid. In humans, as well as cattle, sperm are naturally deposited at the entrance to the cervix and must swim through viscoelastic cervical mucus and other mucoid secretions to reach the site of fertilization. Collective swimming induced by elasticity may thus facilitate sperm migration and contribute to successful fertilization. We note that almost all biological fluids (e.g. mucus and blood) are viscoelastic in nature, and this finding highlights the importance of fluid elasticity in biological function.

Effect of body deformability on microswimming

In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we run immersed-boundary-lattice-Boltzmann simulations of a microswimmer composed of deformable beads connected with springs. We find that the same deformations in the beads can result in different effects on the swimming velocity, namely an enhancement or a reduction, depending on the other parameters. To understand this we determine analytically the velocity of the swimmer, starting from the forces driving the motion and assuming that the deformations in the beads are known as functions of time and are much smaller than the beads themselves. We find that to the lowest order, only the driving frequency mode of the surface deformations contributes to the swimming velocity, and comparison to the simulations shows that both the velocity-promoting and velocity-hindering effects of bead deformability are reproduced correctly by the theory in the limit of small bead deformations. For the case of active deformations we show that there are critical values of the spring constant - which for a general swimmer corresponds to its main elastic degree of freedom - which decide whether the body deformability is beneficial for motion or not.

Maximizing propulsive thrust of a driven filament at low Reynolds number via variable flexibility

At low Reynolds numbers the locomotive capability of a body can be dramatically hindered by the absence of inertia. In this work, we show how propulsive performance in this regime can be significantly enhanced by employing spatially varying flexibility. As a prototypical example, we consider the propulsive thrust generated by a filament periodically driven at one end. The rigid case leads to zero propulsion, as so constrained by Purcell's scallop theorem, while for uniform filaments there exists a bending stiffness maximizing the propulsive force at a given frequency; here we demonstrate explicitly how considerable further improvement can be achieved by simply varying the stiffness along the filament. The optimal flexibility distribution is strongly configuration-dependent: while increasing the flexibility towards the tail-end enhances the propulsion of a clamped filament, for a hinged filament decreasing the flexibility towards the tail-end is instead favorable. The results reveal new design principles for maximizing propulsion at low Reynolds numbers, potentially useful for developing synthetic micro-swimmers requiring large propulsive force for various biomedical applications.

Collective Motion of Microorganisms in a Viscoelastic Fluid

We study the collective motion of a suspension of rodlike microswimmers in a two-dimensional film of viscoelastic fluids. We find that the fluid elasticity has a small effect on a suspension of pullers, while it significantly affects the pushers. The attraction and orientational ordering of the pushers are enhanced in viscoelastic fluids. The induced polymer stresses break down the large-scale flow structures and suppress velocity fluctuations. In addition, the energy spectra and induced mixing in the suspension of pushers are greatly modified by fluid elasticity.

Helicobacter pylori Couples Motility and Diffusion to Actively Create a Heterogeneous Complex Medium in Gastric Mucus

Helicobacter pylori swims through mucus gel by generating ammonia that locally neutralizes the acidic gastric environment, turning nearby gel into a fluid pocket. The size of the fluid zone is important for determining the physics of the motility: in a large zone swimming occurs as in a fluid through hydrodynamic principles, while in a very small zone the motility could be strongly influenced by nonhydrodynamic cell-mucus interactions including chemistry and adhesion. Here, we calculate the size of the fluid pocket. We model how swimming depends on the de-gelation range using a Taylor sheet swimming through a layer of Newtonian fluid bounded by a Brinkman fluid. Then, we model how the de-gelation range depends on the swimming speed by considering the advection-diffusion of ammonia exuded from a translating sphere. Self-consistency between both models determines the values of the swimming speed and the de-gelation range. We find that H. pylori swims through mucus as if unconfined, in a large pocket of Newtonian fluid.

Dynamics of Self-Propelled Janus Particles in Viscoelastic Fluids

We experimentally investigate active motion of spherical Janus colloidal particles in a viscoelastic fluid. Self-propulsion is achieved by a local concentration gradient of a critical polymer mixture which is imposed by laser illumination. Even in the regime where the fluid's viscosity is independent of the deformation rate induced by the particle, we find a remarkable increase of up to 2 orders of magnitude of the rotational diffusion with increasing particle velocity, which can be phenomenologically described by an effective rotational diffusion coefficient dependent on the Weissenberg number. We show that this effect gives rise to a highly anisotropic response of microswimmers in viscoelastic media to external forces, depending on its orientation.

Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time τ(C). To explore the resulting interplay between active and polymeric dynamics, we first generalize a linear stability analysis (from earlier studies without polymer) to derive criteria for the onset of spontaneous heterogeneous flows (strain rate) and/or deformations (strain). We find two modes of instability. The first is a viscous mode, associated with strain rate perturbations. It dominates for relatively small values of τ(C) and is a simple generalization of the instability known previously without polymer. The second is an elastomeric mode, associated with strain perturbations, which dominates at large τ(C) and persists even as τ(C)→∞. We explore the dynamical states to which these instabilities lead by means of direct numerical simulations. These reveal oscillatory shear-banded states in one dimension and activity-driven turbulence in two dimensions even in the elastomeric limit τ(C)→∞. Adding polymer can also have calming effects, increasing the net throughput of spontaneous flow along a channel in a type of drag reduction. The effect of including strong antagonistic coupling between the nematic and polymer is examined numerically, revealing a rich array of spontaneously flowing states.

Efficient nematode swimming in a shear thinning colloidal suspension

The swimming behavior of a nematode Caenorhabditis elegans (C. elegans) is investigated in a non-Newtonian shear thinning colloidal suspension. At the onset value (ϕ∼ 8%), the suspension begins to exhibit shear thinning behavior, and the average swimming speed of worms jumps by approximately 12% more than that measured in a Newtonian solution exhibiting no shear dependent viscosity. In the shear thinning regime, we observe a gradual yet significant improvement in swimming efficiency with an increase in ϕ while the swimming speed remains nearly constant. We postulate that this enhanced swimming can be explained by the temporal change in the stroke form of the nematode that is uniquely observed in a shear thinning colloidal suspension: the nematode features a fast and large stroke in its head to overcome the temporally high drag imposed by the viscous medium, whose effective viscosity (ηs) is shown to drop drastically, inversely proportional to the strength of its stroke. Our results suggest new insights into how nematodes efficiently maneuver through the complex fluid environment in their natural habitat.

Upstream Swimming in Microbiological Flows

Interactions between microorganisms and their complex flowing environments are essential in many biological systems. We develop a model for microswimmer dynamics in non-Newtonian Poiseuille flows. We predict that swimmers in shear-thickening (-thinning) fluids migrate upstream more (less) quickly than in Newtonian fluids and demonstrate that viscoelastic normal stress differences reorient swimmers causing them to migrate upstream at the centerline, in contrast to well-known boundary accumulation in quiescent Newtonian fluids. Based on these observations, we suggest a sorting mechanism to select microbes by swimming speed.

Helicobacter pylori strains vary cell shape and flagellum number to maintain robust motility in viscous environments

The helical shape of the human stomach pathogen Helicobacter pylori has been suggested to provide mechanical advantage for penetrating the viscous stomach mucus layer. Using single-cell tracking and quantitative morphology analysis, we document marked variation in cell body helical parameters and flagellum number among H. pylori strains leading to distinct and broad speed distributions in broth and viscous gastric mucin media. These distributions reflect both temporal variation in swimming speed and morphologic variation within the population. Isogenic mutants with straight-rod morphology showed 7-21% reduction in speed and a lower fraction of motile bacteria. Mutational perturbation of flagellum number revealed a 19% increase in speed with 4 versus 3 median flagellum number. Resistive force theory modeling incorporating variation of both cell shape and flagellum number predicts qualitative speed differences of 10-30% among strains. However, quantitative comparisons suggest resistive force theory underestimates the influence of cell body shape on speed for helical shaped bacteria.

Microscale locomotion in a nematic liquid crystal

Microorganisms often encounter anisotropy, for example in mucus and biofilms. We study how anisotropy and elasticity of the ambient fluid affects the speed of a swimming microorganism with a prescribed stroke. Motivated by recent experiments on swimming bacteria in anisotropic environments, we extend a classical model for swimming microorganisms, the Taylor swimming sheet, actuated by small-amplitude traveling waves in a three-dimensional nematic liquid crystal without twist. We calculate the swimming speed and entrained volumetric flux as a function of the swimmer's stroke properties as well as the elastic and rheological properties of the liquid crystal. These results are then compared to previous results on an analogous swimmer in a hexatic liquid crystal, indicating large differences in the cases of small Ericksen number and in a nematic fluid when the tumbling parameter is near the transition to a shear-aligning nematic. We also propose a novel method of swimming or pumping in a nematic fluid by passing a traveling wave of director oscillation along a rigid wall.

Enzymatically active biomimetic micropropellers for the penetration of mucin gels

In the body, mucus provides an important defense mechanism by limiting the penetration of pathogens. It is therefore also a major obstacle for the efficient delivery of particle-based drug carriers. The acidic stomach lining in particular is difficult to overcome because mucin glycoproteins form viscoelastic gels under acidic conditions. The bacterium Helicobacter pylori has developed a strategy to overcome the mucus barrier by producing the enzyme urease, which locally raises the pH and consequently liquefies the mucus. This allows the bacteria to swim through mucus and to reach the epithelial surface. We present an artificial system of reactive magnetic micropropellers that mimic this strategy to move through gastric mucin gels by making use of surface-immobilized urease. The results demonstrate the validity of this biomimetic approach to penetrate biological gels, and show that externally propelled microstructures can actively and reversibly manipulate the physical state of their surroundings, suggesting that such particles could potentially penetrate native mucus.

Locomotion of a microorganism in weakly viscoelastic liquids

In the present work we study the motion of microorganisms swimming by an axisymmetric distribution of surface tangential velocity in a weakly viscoelastic fluid. The second-order fluid constitutive equation is used to model the suspending fluid, while the well-known "squirmer model" [M. J. Lighthill, Comm. Pure Appl. Math. 5, 109 (1952); J. R. Blake, J. Fluid Mech. 46, 199 (1971)] is employed to describe the organism propulsion mechanism. A regular perturbation expansion up to first order in the Deborah number is performed, and the generalized reciprocity theorem from Stokes flow theory is then used, to derive analytical formulas for the squirmer velocity. Results show that "neutral" squirmers are unaffected by viscoelasticity, whereas "pullers" and "pushers" are slowed down and hastened, respectively. The power dissipated by the swimming microorganism and the "swimming efficiency" are also analytically quantified.

Running and tumbling with E. coli in polymeric solutions

Run-and-tumble motility is widely used by swimming microorganisms including numerous prokaryotic and eukaryotic organisms. Here, we experimentally investigate the run-and-tumble dynamics of the bacterium E. coli in polymeric solutions. We find that even small amounts of polymer in solution can drastically change E. coli dynamics: cells tumble less and their velocity increases, leading to an enhancement in cell translational diffusion and a sharp decline in rotational diffusion. We show that suppression of tumbling is due to fluid viscosity while the enhancement in swimming speed is mainly due to fluid elasticity. Visualization of single fluorescently labeled DNA polymers reveals that the flow generated by individual E. coli is sufficiently strong to stretch polymer molecules and induce elastic stresses in the fluid, which in turn can act on the cell in such a way to enhance its transport. Our results show that the transport and spread of chemotactic cells can be independently modified and controlled by the fluid material properties.

Phase-separation models for swimming enhancement in complex fluids

Swimming cells often have to self-propel through fluids displaying non-Newtonian rheology. While past theoretical work seems to indicate that stresses arising from complex fluids should systematically hinder low-Reynolds number locomotion, experimental observations suggest that locomotion enhancement is possible. In this paper we propose a physical mechanism for locomotion enhancement of microscopic swimmers in a complex fluid. It is based on the fact that microstructured fluids will generically phase-separate near surfaces, leading to the presence of low-viscosity layers, which promote slip and decrease viscous friction near the surface of the swimmer. We use two models to address the consequence of this phase separation: a nonzero apparent slip length for the fluid and then an explicit modeling of the change of viscosity in a thin layer near the swimmer. Considering two canonical setups for low-Reynolds number locomotion, namely the waving locomotion of a two-dimensional sheet and that of a three-dimensional filament, we show that phase-separation systematically increases the locomotion speeds, possibly by orders of magnitude. We close by confronting our predictions with recent experimental results.

Physics of microswimmers--single particle motion and collective behavior: a review

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.

Interactions of highly and low virulent Flavobacterium columnare isolates with gill tissue in carp and rainbow trout

The interactions of Flavobacterium columnare isolates of different virulence with the gills of carp (Cyprinus carpio L.) and rainbow trout (Oncorhynchus mykiss Walbaum) were investigated. Both fish species were exposed to different high (HV) or low virulence (LV) isolates and sacrificed at seven predetermined times post-challenge. Histopathological and ultrastructural examination of carp and rainbow trout inoculated with the HV-isolate disclosed bacterial invasion and concomitant destruction of the gill tissue, gradually spreading from the filament tips towards the base, with outer membrane vesicles surrounding most bacterial cells. In carp, 5-10% of the fish inoculated with the LV-isolate became moribund and their gill tissue displayed the same features as described for the HV-isolate, albeit to a lesser degree. The bacterial numbers retrieved from the gill tissue were significantly higher for HV- compared to LV-isolate challenged carp and rainbow trout. TUNEL-stained and caspase-3-immunostained gill sections demonstrated significantly higher apoptotic cell counts in carp and rainbow trout challenged with the HV-isolate compared to control animals. Periodic acid-Schiff/alcian blue staining demonstrated a significantly higher total gill goblet cell count for HV- and LV-isolate challenged compared to control carp. Moreover, bacterial clusters were embedded in a neutral matrix while being encased by acid mucins, resembling biofilm formation. Eosinophilic granular cell counts were significantly higher in the HV-isolate compared to LV-isolate inoculated and control carp. The present data indicate a high colonization capacity, and the destructive and apoptotic-promoting features of the HV-isolate, and point towards important dynamic host mucin–F. columnare interactions warranting further research.