Bacteria-inspired magnetically actuated rod-like soft robot in viscous fluids.

This paper seeks to design, develop, and explore the locomotive dynamics and morphological adaptability of a bacteria-inspired rod-like soft robot propelled in highly viscous Newtonian fluids. The soft robots were fabricated as tapered, hollow rod-like soft scaffolds by applying a robust and economic molding technique to a polyacrylamide-based hydrogel polymer. Cylindrical micro-magnets were embedded in both ends of the soft scaffolds, which allowed bending (deformation) and actuation under a uniform rotating magnetic field. We demonstrated that the tapered rod-like soft robot in viscous Newtonian fluids could perform two types of propulsion; boundary rolling was displayed when the soft robot was located near a boundary, and swimming was displayed far away from the boundary. In addition, we performed numerical simulations to understand the swimming propulsion along the rotating axis and the way in which this propulsion is affected by the soft robot's design, rotation frequency, and fluid viscosity. Our results suggest that a simple geometrical asymmetry enables the rod-like soft robot to perform propulsion in the low Reynolds number (Re≪ 1) regime; these promising results provide essential insights into the improvements that must be made to integrate the soft robots into minimally invasivein vivoapplications.

Symmetry breaking propulsion of magnetic microspheres in nonlinearly viscoelastic fluids.

Microscale propulsion impacts a diverse array of fields ranging from biology and ecology to health applications, such as infection, fertility, drug delivery, and microsurgery. However, propulsion in such viscous drag-dominated fluid environments is highly constrained, with time-reversal and geometric symmetries ruling out entire classes of propulsion. Here, we report the spontaneous symmetry-breaking propulsion of rotating spherical microparticles within non-Newtonian fluids. While symmetry analysis suggests that propulsion is not possible along the fore-aft directions, we demonstrate the existence of two equal and opposite propulsion states along the sphere's rotation axis. We propose and experimentally corroborate a propulsion mechanism for these spherical microparticles, the simplest microswimmers to date, arising from nonlinear viscoelastic effects in rotating flows similar to the rod-climbing effect. Similar possibilities of spontaneous symmetry-breaking could be used to circumvent other restrictions on propulsion, revising notions of microrobotic design and control, drug delivery, microscale pumping, and locomotion of microorganisms.

Bipolar lophotrichous Helicobacter suis combine extended and wrapped flagella bundles to exhibit multiple modes of motility.

The swimming strategies of unipolar flagellated bacteria are well known but little is known about how bipolar bacteria swim. Here we examine the motility of Helicobacter suis, a bipolar gastric-ulcer-causing bacterium that infects pigs and humans. Phase-contrast microscopy of unlabeled bacteria reveals flagella bundles in two conformations, extended away from the body (E) or flipped backwards and wrapped (W) around the body. We captured videos of the transition between these two states and observed three different swimming modes in broth: with one bundle rotating wrapped around the body and the other extended (EW), both extended (EE), and both wrapped (WW). Only EW and WW modes were seen in porcine gastric mucin. The EW mode displayed ballistic trajectories while the other two displayed superdiffusive random walk trajectories with slower swimming speeds. Separation into these two categories was also observed by tracking the mean square displacement of thousands of trajectories at lower magnification. Using the Method of Regularized Stokeslets we numerically calculate the swimming dynamics of these three different swimming modes and obtain good qualitative agreement with the measurements, including the decreased speed of the less frequent modes. Our results suggest that the extended bundle dominates the swimming dynamics.

Bacteria-inspired nanorobots with flagellar polymorphic transformations and bundling.

Wirelessly controlled nanoscale robots have the potential to be used for both in vitro and in vivo biomedical applications. So far, the vast majority of reported micro- and nanoscale swimmers have taken the approach of mimicking the rotary motion of helical bacterial flagella for propulsion, and are often composed of monolithic inorganic materials or photoactive polymers. However, currently no man-made soft nanohelix has the ability to rapidly reconfigure its geometry in response to multiple forms of environmental stimuli, which has the potential to enhance motility in tortuous heterogeneous biological environments. Here, we report magnetic actuation of self-assembled bacterial flagellar nanorobotic swimmers. Bacterial flagella change their helical form in response to environmental stimuli, leading to a difference in propulsion before and after the change in flagellar form. We experimentally and numerically characterize this response by studying the swimming of three flagellar forms. Also, we demonstrate the ability to steer these devices and induce flagellar bundling in multi-flagellated nanoswimmers.

Traction reveals mechanisms of wall effects for microswimmers near boundaries.

The influence of a plane boundary on low-Reynolds-number swimmers has frequently been studied using image systems for flow singularities. However, the boundary effect can also be expressed using a boundary integral representation over the traction on the boundary. We show that examining the traction pattern on the boundary caused by a swimmer can yield physical insights into determining when far-field multipole models are accurate. We investigate the swimming velocities and the traction of a three-sphere swimmer initially placed parallel to an infinite planar wall. In the far field, the instantaneous effect of the wall on the swimmer is well approximated by that of a multipole expansion consisting of a force dipole and a force quadrupole. On the other hand, the swimmer close to the wall must be described by a system of singularities reflecting its internal structure. We show that these limits and the transition between them can be independently identified by examining the traction pattern on the wall, either using a quantitative correlation coefficient or by visual inspection. Last, we find that for nonconstant propulsion, correlations between swimming stroke motions and internal positions are important and not captured by time-averaged traction on the wall, indicating that care must be taken when applying multipole expansions to study boundary effects in cases of nonconstant propulsion.

Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach.

This study is motivated by a microfluidic device that imparts a magnetic torque on an array of bacterial flagella. Bacterial flagella can transform their helical geometry autonomously in response to properties of the background fluid, which provides an intriguing mechanism allowing their use as an engineered element for the regulation or transport of chemicals in microscale applications. The synchronization of flagellar phase has been widely studied in biological contexts, but here we examine the synchronization of flagellar tilt, which is necessary for effective pumping. We first examine the effects of helical geometry and tilt on the pumping flows generated by a single rotating flagellum. Next, we explore a mean-field model for an array of helical flagella to understand how collective tilt arises and influences pumping. The mean-field methodology allows us to take into account possible phase differences through a time-averaging procedure and to model an infinite array of flagella. We find array separation distances, magnetic field strengths, and rotation frequencies that produce nontrivial self-consistent pumping solutions. For individual flagella, pumping is reversed when helicity or rotation is reversed; in contrast, when collective effects are included, self-consistent tilted pumping solutions become untilted nonpumping solutions when helicity or rotation is reversed.

Helical and rod-shaped bacteria swim in helical trajectories with little additional propulsion from helical shape.

It has frequently been hypothesized that the helical body shapes of flagellated bacteria may yield some advantage in swimming ability. In particular, the helical-shaped pathogen Helicobacter pylori is often claimed to swim like a corkscrew through its harsh gastric habitat, but there has been no direct confirmation or quantification of such claims. Using fast time-resolution and high-magnification two-dimensional (2D) phase-contrast microscopy to simultaneously image and track individual bacteria in bacterial broth as well as mucin solutions, we show that both helical and rod-shaped H. pylori rotated as they swam, producing a helical trajectory. Cell shape analysis enabled us to determine shape as well as the rotational and translational speed for both forward and reverse motions, thereby inferring flagellar kinematics. Using the method of regularized Stokeslets, we directly compare observed speeds and trajectories to numerical calculations for both helical and rod-shaped bacteria in mucin and broth to validate the numerical model. Although experimental observations are limited to select cases, the model allows quantification of the effects of body helicity, length, and diameter. We find that due to relatively slow body rotation rates, the helical shape makes at most a 15% contribution to propulsive thrust. The effect of body shape on swimming speeds is instead dominated by variations in translational drag required to move the cell body. Because helical cells are one of the strongest candidates for propulsion arising from the cell body, our results imply that quite generally, swimming speeds of flagellated bacteria can only be increased a little by body propulsion.

Magnetization directions and geometries of helical microswimmers for linear velocity-frequency response.

Recently, there has been much progress in creating microswimmers or microrobots capable of controlled propulsion in fluidic environments. These microswimmers have numerous possible applications in biomedicine, microfabrication, and sensing. One type of effective microrobot consists of rigid magnetic helical microswimmers that are propelled when rotated at a range of frequencies by an external rotating magnetic field. Here we focus on investigating which magnetic dipoles and helical geometries optimally lead to linear velocity-frequency response, which may be desirable for the precise control and positioning of microswimmers. We identify a class of optimal magnetic field moments. We connect our results to the wobbling behavior previously observed and studied in helical microswimmers. In contrast to previous studies, we find that when the full helical geometry is taken into account, wobble-free motion is not possible for magnetic fields rotating in a plane. Our results compare well quantitatively to previously reported experiments, validating the theoretical analysis method. Finally, in the context of our optimal moments, we identify helical geometries for minimization of wobbling and maximization of swimming velocities.

Prospective study on the effects of orthotic treatment for medial knee osteoarthritis in Chinese patients: clinical outcome and gait analysis.

OBJECTIVE: To evaluate the effectiveness of various orthotic treatments for patients with isolated medial compartment osteoarthritis. DESIGN: Prospective cohort study with sequential interventions. SETTING: University-affiliated hospital, Hong Kong. PATIENTS: From December 2010 to November 2011, 10 patients with medial knee osteoarthritis were referred by orthopaedic surgeons for orthotic treatment. All patients were sequentially treated with flat insole, lateral-wedged insole, lateral-wedged insole with subtalar strap, lateral-wedged insole with arch support, valgus knee brace, and valgus knee brace with lateral-wedged insole with arch support for 4 weeks with no treatment break. Three-dimensional gait analysis and questionnaires were completed after each orthotic treatment. MAIN OUTCOME MEASURES: The Western Ontario and McMaster Universities Arthritis Index (WOMAC), visual analogue scale scores, and peak and mean knee adduction moments. RESULTS: Compared with pretreatment, the lateral-wedged insole, lateral-wedged insole with arch support, and valgus knee brace groups demonstrated significant reductions in WOMAC pain score (19.1%, P=0.04; 18.2%, P=0.04; and 20.4%, P=0.02, respectively). The lateral-wedged insole with arch support group showed the greatest reduction in visual analogue scale score compared with pretreatment at 24.1% (P=0.004). Addition of a subtalar strap to lateral-wedged insoles (lateral-wedged insole with subtalar strap) did not produce significant benefit when compared with the lateral-wedged insole alone. The valgus knee brace with lateral-wedged insole with arch support group demonstrated an additive effect with a statistically significant reduction in WOMAC total score (-26.7%, P=0.01). Compliance with treatment for the isolated insole groups were all over 90%, but compliance for the valgus knee brace-associated groups was only around 50%. Gait analysis indicated statistically significant reductions in peak and mean knee adduction moments in all orthotic groups when compared with a flat insole. CONCLUSIONS: These results support the use of orthotic treatment for early medial compartment knee osteoarthritis.

Swimming fluctuations of micro-organisms due to heterogeneous microstructure.

Swimming microorganisms in biological complex fluids may be greatly influenced by heterogeneous media and microstructure with length scales comparable to the organisms. A fundamental effect of swimming in a heterogeneous rather than homogeneous medium is that variations in local environments lead to swimming velocity fluctuations. Here we examine long-range hydrodynamic contributions to these fluctuations using a Najafi-Golestanian swimmer near spherical and filamentous obstacles. We find that forces on microstructures determine changes in swimming speed. For macroscopically isotropic networks, we also show how the variance of the fluctuations in swimming speeds are related to density and orientational correlations in the medium.

Speed of a swimming sheet in Newtonian and viscoelastic fluids.

We measure the swimming speed of a cylindrical version of Taylor's swimming sheet in viscoelastic fluids, and find that depending on the rheology, the speed can either increase or decrease relative to the speed in a Newtonian viscous fluid. The swimming stroke of the sheet is a prescribed propagating wave that travels along the sheet in the azimuthal direction. The measurements are performed with the sheet immersed in a fluid inside a cylindrical tank under torque-free conditions. Swimming speeds in the Newtonian case are found to be consistent with calculations using the Stokes equation. A faster swimming speed is found in a viscoelastic fluid that has a viscosity independent of shear rate. By contrast, a slower swimming speed is found with more complex shear-thinning viscoelastic fluids which have multiple relaxation time scales as well. These results are compared with calculations with Oldroyd-B fluids which find a decreasing swimming speed with Deborah number given by the product of the fluid elastic relaxation time scale and the driving frequency.

Bacterial rheotaxis.

The motility of organisms is often directed in response to environmental stimuli. Rheotaxis is the directed movement resulting from fluid velocity gradients, long studied in fish, aquatic invertebrates, and spermatozoa. Using carefully controlled microfluidic flows, we show that rheotaxis also occurs in bacteria. Excellent quantitative agreement between experiments with Bacillus subtilis and a mathematical model reveals that bacterial rheotaxis is a purely physical phenomenon, in contrast to fish rheotaxis but in the same way as sperm rheotaxis. This previously unrecognized bacterial taxis results from a subtle interplay between velocity gradients and the helical shape of flagella, which together generate a torque that alters a bacterium's swimming direction. Because this torque is independent of the presence of a nearby surface, bacterial rheotaxis is not limited to the immediate neighborhood of liquid-solid interfaces, but also takes place in the bulk fluid. We predict that rheotaxis occurs in a wide range of bacterial habitats, from the natural environment to the human body, and can interfere with chemotaxis, suggesting that the fitness benefit conferred by bacterial motility may be sharply reduced in some hydrodynamic conditions.

The heterogeneous motility of the Lyme disease spirochete in gelatin mimics dissemination through tissue.

The Lyme disease spirochete Borrelia burgdorferi exists in nature in an enzootic cycle that involves the arthropod vector Ixodes scapularis and mammalian reservoirs. To disseminate within and between these hosts, spirochetes must migrate through complex, polymeric environments such as the basement membrane of the tick midgut and the dermis of the mammal. To date, most research on the motility of B. burgdorferi has been done in media that do not resemble the tissue milieus that B. burgdorferi encounter in vivo. Here we show that the motility of Borrelia in gelatin matrices in vitro resembles the pathogen's movements in the chronically infected mouse dermis imaged by intravital microscopy. More specifically, B. burgdorferi motility in mouse dermis and gelatin is heterogeneous, with the bacteria transitioning between at least three different motility states that depend on transient adhesions to the matrix. We also show that B. burgdorferi is able to penetrate matrices with pore sizes much smaller than the diameter of the bacterium. We find a complex relationship between the swimming behavior of B. burgdorferi and the rheological properties of the gelatin, which cannot be accounted for by recent theoretical predictions for microorganism swimming in gels. Our results also emphasize the importance of considering borrelial adhesion as a dynamic rather than a static process.

Separation of microscale chiral objects by shear flow.

We show that plane parabolic flow in a microfluidic channel causes nonmotile, helically shaped bacteria to drift perpendicular to the shear plane. Net drift results from the preferential alignment of helices with streamlines, with a direction that depends on the chirality of the helix and the sign of the shear rate. The drift is in good agreement with a model based on resistive force theory, and separation is efficient (>80%) and fast (<2 s). We estimate the effect of Brownian rotational diffusion on chiral separation and show how this method can be extended to separate chiral molecules.

Swimming speeds of filaments in nonlinearly viscoelastic fluids.

Many micro-organisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on micro-organisms which use flagella for propulsion. We address how swimming velocities are affected in nonlinearly viscoelastic fluids by examining the problem of an infinitely long cylinder with arbitrary beating motion in the Oldroyd-B fluid. We solve for the swimming velocity in the limit in which deflections of the cylinder from its straight configuration are small relative to the radius of the cylinder and the wavelength of the deflections; furthermore, the radius of the cylinder is small compared to the wavelength of deflections. We find that swimming velocities are diminished by nonlinear viscoelastic effects. We apply these results to examine what types of swimming motions can produce net translation in a nonlinear fluid, comparing to the Newtonian case, for which Purcell's "scallop" theorem describes how time-reversibility constrains which swimming motions are effective. We find that a leading order violation of the scallop theorem occurs for reciprocal motions in which the backward and forward strokes occur at different rates.

Beating patterns of filaments in viscoelastic fluids.

Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella.

Role of slip between a probe particle and a gel in microrheology.

In the technique of microrheology, macroscopic rheological parameters as well as information about local structure are deduced from the behavior of microscopic probe particles under thermal or active forcing. Microrheology requires knowledge of the relation between macroscopic parameters and the force felt by a particle in response to displacements. We investigate this response function for a spherical particle using the two-fluid model, in which the gel is represented by a polymer network coupled to a surrounding solvent via a drag force. We obtain an analytic solution for the response function in the limit of small volume fraction of the polymer network, and neglecting inertial effects. We use no-slip boundary conditions for the solvent at the surface of the sphere. The boundary condition for the network at the surface of the sphere is a kinetic friction law, for which the tangential stress of the network is proportional to relative velocity of the network and the sphere. This boundary condition encompasses both no-slip and frictionless boundary conditions as limits. Far from the sphere there is no relative motion between the solvent and network due to the coupling between them. However, the different boundary conditions on the solvent and network tend to produce different far-field motions. We show that the far-field motion and the force on the sphere are controlled by the solvent boundary conditions at high frequency and by the network boundary conditions at low frequency. At low frequencies compression of the network can also affect the force on the sphere. We find the crossover frequencies at which the effects of sliding of the sphere past the polymer network and compression of the gel become important. The effects of sliding alone can lead to an underestimation of moduli by up to 33%, while the effects of compression alone can lead to an underestimation of moduli by up to 20%, and the effects of sliding and compression combined can lead to an underestimation of moduli by up to 43%.

Theory of swimming filaments in viscoelastic media.

Motivated by our desire to understand the biophysical mechanisms underlying the swimming of sperm in the non-Newtonian fluids of the female mammalian reproductive tract, we examine the swimming of filaments in the nonlinear viscoelastic upper convected Maxwell model. We obtain the swimming velocity and hydrodynamic force exerted on an infinitely long cylinder with prescribed beating pattern. We use these results to examine the swimming of a simplified sliding-filament model for a sperm flagellum. Viscoelasticity tends to decrease swimming speed, and changes in the beating patterns due to viscoelasticity can reverse swimming direction.

Stabilizing superconductivity in nanowires by coupling to dissipative environments.

We present a theory for a finite-length superconducting nanowire coupled to an environment. We show that in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to explain the "antiproximity effect" recently seen by Tian et al. in zinc nanowires.