Feedback Control of an Achiral Robotic Microswimmer

Magnetic microswimmers are useful for navigating and performing tasks at small scales.To demonstrate effective control over such microswimmers,we implemented feedback control of the three-bead achiral microswimmers in both simulation and experiment.The achiral microswimmers with the ability to swim in bulk fluid are controlled wirelessly using magnetic fields generated from electromagnetic coils.The achirality of the microswimmers introduces unknown handedness resulting in uncertainty in swimming direction.We use a combination of rotating and static magnetic fields generated from an approximate Helmholtz coil system to overcome such uncertainty.There are also movement uncertainties due to environmental factors such as unsteady flow conditions.A kinematic model based feedback controller was created based on data fitting of experimental data.However,the controller was unable to yield satisfactory performance due to uncertainties from environmental factors;i.e.,the time to reach target pose under adverse flow condition is too long.Following the implementation of an integral controller to control the microswimmers' swimming velocity,the microswimmers were able to reach the target in roughly half the time.Through simulation and experiments,we show that the feedback control law can move an achiral microswimmer from any initial conditions to a target pose.     

Trypanosome Motion Represents an Adaptation to the Crowded Environment of the Vertebrate Bloodstream

Blood is a remarkable habitat: it is highly viscous, contains a dense packaging of cells and perpetually flows at velocities varying over three orders of magnitude. Only few pathogens endure the harsh physical conditions within the vertebrate bloodstream and prosper despite being constantly attacked by host antibodies. African trypanosomes are strictly extracellular blood parasites, which evade the immune response through a system of antigenic variation and incessant motility. How the flagellates actually swim in blood remains to be elucidated. Here, we show that the mode and dynamics of trypanosome locomotion are a trait of life within a crowded environment. Using high-speed fluorescence microscopy and ordered micro-pillar arrays we show that the parasites mode of motility is adapted to the density of cells in blood. Trypanosomes are pulled forward by the planar beat of the single flagellum. Hydrodynamic flow across the asymmetrically shaped cell body translates into its rotational movement. Importantly, the presence of particles with the shape, size and spacing of blood cells is required and sufficient for trypanosomes to reach maximum forward velocity. If the density of obstacles, however, is further increased to resemble collagen networks or tissue spaces, the parasites reverse their flagellar beat and consequently swim backwards, in this way avoiding getting trapped. In the absence of obstacles, this flagellar beat reversal occurs randomly resulting in irregular waveforms and apparent cell tumbling. Thus, the swimming behavior of trypanosomes is a surprising example of micro-adaptation to life at low Reynolds numbers. For a precise physical interpretation, we compare our high-resolution microscopic data to results from a simulation technique that combines the method of multi-particle collision dynamics with a triangulated surface model. The simulation produces a rotating cell body and a helical swimming path, providing a functioning simulation method for a microorganism with a complex swimming strategy.     

Hydrodynamic flow-mediated protein sorting on the cell surface of trypanosomes

The unicellular parasite Trypanosoma brucei rapidly removes host-derived immunoglobulin (Ig) from its cell surface, which is dominated by a single type of glycosylphosphatidylinositol-anchored variant surface glycoprotein (VSG). We have determined the mechanism of antibody clearance and found that Ig-VSG immune complexes are passively sorted to the posterior cell pole, where they are endocytosed. The backward movement of immune complexes requires forward cellular motility but is independent of endocytosis and of actin function. We suggest that the hydrodynamic flow acting on swimming trypanosomes causes directional movement of Ig-VSG immune complexes in the plane of the plasma membrane, that is, immunoglobulins attached to VSG function as molecular sails. Protein sorting by hydrodynamic forces helps to protect trypanosomes against complement-mediated immune destruction in culture and possibly in infected mammals but likewise may be of functional significance at the surface of other cell types such as epithelial cells lining blood vessels.     

The Orientation of Swimming Biflagellates in Shear Flows

Biflagellated algae swim in mean directions that are governed by their environments. For example, many algae can swim upward on average (gravitaxis) and toward downwelling fluid (gyrotaxis) via a variety of mechanisms. Accumulations of cells within the fluid can induce hydrodynamic instabilities leading to patterns and flow, termed bioconvection, which may be of particular relevance to algal bioreactors and plankton dynamics. Furthermore, knowledge of the behavior of an individual swimming cell subject to imposed flow is prerequisite to a full understanding of the scaled-up bulk behavior and population dynamics of cells in oceans and lakes; swimming behavior and patchiness will impact opportunities for interactions, which are at the heart of population models. Hence, better estimates of population level parameters necessitate a detailed understanding of cell swimming bias. Using the method of regularized Stokeslets, numerical computations are developed to investigate the swimming behavior of and fluid flow around gyrotactic prolate spheroidal biflagellates with five distinct flagellar beats. In particular, we explore cell reorientation mechanisms associated with bottom-heaviness and sedimentation and find that they are commensurate and complementary. Furthermore, using an experimentally measured flagellar beat for Chlamydomonas reinhardtii, we reveal that the effective cell eccentricity of the swimming cell is much smaller than for the inanimate body alone, suggesting that the cells may be modeled satisfactorily as self-propelled spheres. Finally, we propose a method to estimate the effective cell eccentricity of any biflagellate when flagellar beat images are obtained haphazardly.     

Swimming Behavior of Pseudomonas aeruginosa Studied by Holographic 3D Tracking

Holographic 3D tracking was applied to record and analyze the swimming behavior of Pseudomonas aeruginosa. The obtained trajectories allow to qualitatively and quantitatively analyze the free swimming behavior of the bacterium. This can be classified into five distinct swimming patterns. In addition to the previously reported smooth and oscillatory swimming motions, three additional patterns are distinguished. We show that Pseudomonas aeruginosa performs helical movements which were so far only described for larger microorganisms. Occurrence of the swimming patterns was determined and transitions between the patterns were analyzed.     

Two-dimensional motion of Brownian swimmers in linear flows

The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations.     

Motility analysis of circularly swimming bull spermatozoa by quasi-elastic light scattering and cinematography.

The Rayleigh-Gans-Debye approximation is used to predict the electric field autocorrelation functions of light scattered from circularly swimming bull spermatozoa. Using parameters determined from cinematography and modeling the cells as coated ellipsoids of semiaxes a = 0.5 micrometers, b = 2.3 micrometers, and c = 9.0 micrometers, we were able to obtain model spectra that mimic the data exactly. A coat is found to be a necessary attribute of the particle. It is also clear that these model functions at 15 degrees may be represented by the relatively simple function used before by Hallett et al. (1978) to fit data from circularly swimming cells, thus giving some physical meaning to these functional shapes. Because of this agreement the half-widths of experimental functions can now be interpreted in terms of an oscillatory frequency for the movement of the circularly swimming cell. The cinematographic results show a trend to chaotic behavior as the temperature of the sample is increased, with concomitant decrease in overall efficiency. This is manifested by a decrease in oscillatory frequency and translational speed.     

Experimental Studies and Dynamics Modeling Analysis of the Swimming and Diving of Whirligig Beetles (Coleoptera: Gyrinidae)

Whirligig beetles (Coleoptera, Gyrinidae) can fly through the air, swiftly swim on the surface of water, and quickly dive across the air-water interface. The propulsive efficiency of the species is believed to be one of the highest measured for a thrust generating apparatus within the animal kingdom. The goals of this research were to understand the distinctive biological mechanisms that allow the beetles to swim and dive, while searching for potential bio-inspired robotics applications. Through static and dynamic measurements obtained using a combination of microscopy and high-speed imaging, parameters associated with the morphology and beating kinematics of the whirligig beetle''s legs in swimming and diving were obtained. Using data obtained from these experiments, dynamics models of both swimming and diving were developed. Through analysis of simulations conducted using these models it was possible to determine several key principles associated with the swimming and diving processes. First, we determined that curved swimming trajectories were more energy efficient than linear trajectories, which explains why they are more often observed in nature. Second, we concluded that the hind legs were able to propel the beetle farther than the middle legs, and also that the hind legs were able to generate a larger angular velocity than the middle legs. However, analysis of circular swimming trajectories showed that the middle legs were important in maintaining stable trajectories, and thus were necessary for steering. Finally, we discovered that in order for the beetle to transition from swimming to diving, the legs must change the plane in which they beat, which provides the force required to alter the tilt angle of the body necessary to break the surface tension of water. We have further examined how the principles learned from this study may be applied to the design of bio-inspired swimming/diving robots.     

Analyzing fish movement as a persistent turning walker

The trajectories of Kuhlia mugil fish swimming freely in a tank are analyzed in order to develop a model of spontaneous fish movement. The data show that K. mugil displacement is best described by turning speed and its auto-correlation. The continuous-time process governing this new kind of displacement is modelled by a stochastic differential equation of Ornstein–Uhlenbeck family: the persistent turning walker. The associated diffusive dynamics are compared to the standard persistent random walker model and we show that the resulting diffusion coefficient scales non-linearly with linear swimming speed. In order to illustrate how interactions with other fish or the environment can be added to this spontaneous movement model we quantify the effect of tank walls on the turning speed and adequately reproduce the characteristics of the observed fish trajectories.     

Modeling the influence of optic flow on grid cell firing in the absence of other cues1

Information from the vestibular, sensorimotor, or visual systems can affect the firing of grid cells recorded in entorhinal cortex of rats. Optic flow provides information about the rat’s linear and rotational velocity and, thus, could influence the firing pattern of grid cells. To investigate this possible link, we model parts of the rat’s visual system and analyze their capability in estimating linear and rotational velocity. In our model a rat is simulated to move along trajectories recorded from rat’s foraging on a circular ground platform. Thus, we preserve the intrinsic statistics of real rats’ movements. Visual image motion is analytically computed for a spherical camera model and superimposed with noise in order to model the optic flow that would be available to the rat. This optic flow is fed into a template model to estimate the rat’s linear and rotational velocities, which in turn are fed into an oscillatory interference model of grid cell firing. Grid scores are reported while altering the flow noise, tilt angle of the optical axis with respect to the ground, the number of flow templates, and the frequency used in the oscillatory interference model. Activity patterns are compatible with those of grid cells, suggesting that optic flow can contribute to their firing.     

The role of actin cytoskeleton in oscillatory fluid flow-induced signaling in MC3T3-E1 osteoblasts

Fluid flow due to loading in bone is a potent mechanical signal that may play an important role in bone adaptation to its mechanical environment. Previous in vitro studies of osteoblastic cells revealed that the upregulation of cyclooxygenase-2 (COX-2) and c-fos induced by steady fluid flow depends on a change in actin polymerization dynamics and the formation of actin stress fibers. Exposing cells to dynamic oscillatory fluid flow, the temporal flow pattern that results from normal physical activity, is also known to result in increased COX-2 expression and PGE₂ release. The purpose of this study was to determine whether dynamic fluid flow results in changes in actin dynamics similar to steady flow and to determine whether alterations in actin dynamics are required for PGE₂ release. We found that exposure to oscillatory fluid flow did not result in the development of F-actin stress fibers in MC3T3-E1 osteoblastic cells and that inhibition of actin polymerization with cytochalasin D did not inhibit intracellular calcium mobilization or PGE₂ release. In fact, PGE₂ release was increased threefold in the polymerization inhibited cells and this PGE₂ release was dependent on calcium release from the endoplasmic reticulum. This was in contrast to the PGE₂ release that occurs in normal cells, which is independent of calcium flux from endoplasmic reticulum stores. We suggest that this increased PGE₂ release involves a different molecular mechanism perhaps involving increased deformation due to the compromised cytoskeleton. mechanotransduction; cell mechanics     

Copepod flow modes and modulation: a modelling study of the water currents produced by an unsteadily swimming copepod

Video observation has shown that feeding-current-producing calanoid copepods modulate their feeding currents by displaying a sequence of different swimming behaviours during a time period of up to tens of seconds. In order to understand the feeding-current modulation process, we numerically modelled the steady feeding currents for different modes of observed copepod motion behaviours (i.e. free sinking, partial sinking, hovering, vertical swimming upward and horizontal swimming backward or forward). Based on observational data, we also reproduced numerically a modulated feeding current associated with an unsteadily swimming copepod. We found that: (i) by changing its propulsive force, a copepod can switch between different swimming behaviours, leading to completely different flow-field patterns in self-generated surrounding flow; (ii) by exerting a time-varying propulsive force, a copepod can modulate temporally the basic flow modes to create an unsteady feeding current which manipulates precisely the trajectories of entrained food particles over a long time period; (iii) the modulation process may be energetically more efficient than exerting a constant propulsive force onto water to create a constant feeding current of a wider entrainment range. A probable reason is that the modulated unsteady flow entrains those water parcels containing food particles and leaves behind those without valuable food in them.     

Effective shear viscosity and dynamics of suspensions of micro-swimmers from small to moderate concentrations

Recently, there has been a number of experimental studies convincingly demonstrating that a suspension of self-propelled bacteria (microswimmers in general) may have an effective viscosity significantly smaller than the viscosity of the ambient fluid. This is in sharp contrast with suspensions of hard passive inclusions, whose presence always increases the viscosity. Here we present a 2D model for a suspension of microswimmers in a fluid and analyze it analytically in the dilute regime (no swimmer–swimmer interactions) and numerically using a Mimetic Finite Difference discretization. Our analysis shows that in the dilute regime (in the absence of rotational diffusion) the effective shear viscosity is not affected by self-propulsion. But at the moderate concentrations (due to swimmer–swimmer interactions) the effective viscosity decreases linearly as a function of the propulsion strength of the swimmers. These findings prove that (i) a physically observable decrease of viscosity for a suspension of self-propelled microswimmers can be explained purely by hydrodynamic interactions and (ii) self-propulsion and interaction of swimmers are both essential to the reduction of the effective shear viscosity. We also performed a number of numerical experiments analyzing the dynamics of swimmers resulting from pairwise interactions. The numerical results agree with the physically observed phenomena (e.g., attraction of swimmer to swimmer and swimmer to the wall). This is viewed as an additional validation of the model and the numerical scheme.     

A quantitative 3D motility analysis of Trypanosoma brucei by use of digital in-line holographic microscopy

We present a quantitative 3D analysis of the motility of the blood parasite Trypanosoma brucei. Digital in-line holographic microscopy has been used to track single cells with high temporal and spatial accuracy to obtain quantitative data on their behavior. Comparing bloodstream form and insect form trypanosomes as well as mutant and wildtype cells under varying external conditions we were able to derive a general two-state-run-and-tumble-model for trypanosome motility. Differences in the motility of distinct strains indicate that adaption of the trypanosomes to their natural environments involves a change in their mode of swimming.     

The rate of change in Ca(2+) concentration controls sperm chemotaxis

During chemotaxis and phototaxis, sperm, algae, marine zooplankton, and other microswimmers move on helical paths or drifting circles by rhythmically bending cell protrusions called motile cilia or flagella. Sperm of marine invertebrates navigate in a chemoattractant gradient by adjusting the flagellar waveform and, thereby, the swimming path. The waveform is periodically modulated by Ca(2+) oscillations. How Ca(2+) signals elicit steering responses and shape the path is unknown. We unveil the signal transfer between the changes in intracellular Ca(2+) concentration ([Ca(2+)](i)) and path curvature (κ). We show that κ is modulated by the time derivative d[Ca(2+)](i)/dt rather than the absolute [Ca(2+)](i). Furthermore, simulation of swimming paths using various Ca(2+) waveforms reproduces the wealth of swimming paths observed for sperm of marine invertebrates. We propose a cellular mechanism for a chemical differentiator that computes a time derivative. The cytoskeleton of cilia, the axoneme, is highly conserved. Thus, motile ciliated cells in general might use a similar cellular computation to translate changes of [Ca(2+)](i) into motion.     

Anomalies in the motion dynamics of long-flagella mutants of Chlamydomonas reinhardtii

Chlamydomonas reinhardtii has long been used as a model organism in studies of cell motility and flagellar dynamics. The motility of the well-conserved ‘9+2’ axoneme in its flagella remains a subject of immense curiosity. Using high-speed videography and morphological analyses, we have characterized long-flagella mutants (lf1, lf2-1, lf2-5, lf3-2, and lf4) of C. reinhardtii for biophysical parameters such as swimming velocities, waveforms, beat frequencies, and swimming trajectories. These mutants are aberrant in proteins involved in the regulation of flagellar length and bring about a phenotypic increase in this length. Our results reveal that the flagellar beat frequency and swimming velocity are negatively correlated with the length of the flagella. When compared to the wild-type, any increase in the flagellar length reduces both the swimming velocities (by 26–57%) and beat frequencies (by 8–16%). We demonstrate that with no apparent aberrations/ultrastructural deformities in the mutant axonemes, it is this increased length that has a critical role to play in the motion dynamics of C. reinhardtii cells, and, provided there are no significant changes in their flagellar proteome, any increase in this length compromises the swimming velocity either by reduction of the beat frequency or by an alteration in the waveform of the flagella.     

Pelagic-benthic transition of the harmful alga, Heterosigma akashiwo: Changes in swimming and implications for benthic cell distributions

Many harmful algal blooming (HAB) species transition between a vegetative, motile phase in the water column and a dormant, non-motile resting phase in the sediments. These life history transitions potentially regulate the timing, location and persistence of bloom events. Motility promotes aggregation and influences vertical distributions in the water column. However, the contribution of this behavior to benthic distributions of resting cells is currently unknown. We used video-tracking techniques to test the hypothesis that algal cells use active down-swimming during pelagic-benthic transition to favorably influence benthic distributions. In an experimental water column, we monitored cell swimming trajectories of Heterosigma akashiwo for 14 days after cells were signaled to enter the benthic resting stage. Using the statistical characteristics of individual cell trajectories, we developed a video-based motion assay to assign each tracked Heterosigma cell to one of three cell states known to occur during pelagic-benthic transition: induced motile, transitional and resting. The primary swimming characteristic influencing benthic distribution, net vertical velocity, was essentially the same for all three cell states. Hence, we found no evidence that active down-swimming influences benthic distributions. Our data suggest that benthic distributions of Heterosigma resting cells are similar to distributions of slowly sedimenting passive particles. These observations suggest that Heterosigma benthic resting cell distributions can be predicted by modeling the effects of cell sedimentation rates combined with geophysical flow patterns.     

Switching of Swimming Modes in Magnetospirillium gryphiswaldense

The microaerophilic magnetotactic bacterium Magnetospirillum gryphiswaldense swims along magnetic field lines using a single flagellum at each cell pole. It is believed that this magnetotactic behavior enables cells to seek optimal oxygen concentration with maximal efficiency. We analyze the trajectories of swimming M. gryphiswaldense cells in external magnetic fields larger than the earth’s field, and show that each cell can switch very rapidly (in <0.2 s) between a fast and a slow swimming mode. Close to a glass surface, a variety of trajectories were observed, from straight swimming that systematically deviates from field lines to various helices. A model in which fast (slow) swimming is solely due to the rotation of the trailing (leading) flagellum can account for these observations. We determined the magnetic moment of this bacterium using a to our knowledge new method, and obtained a value of (2.0 ± 0.6) × 10^?16 A · m². This value is found to be consistent with parameters emerging from quantitative fitting of trajectories to our model.     

Differential Dynamic Microscopy: A High-Throughput Method for Characterizing the Motility of Microorganisms

We present a fast, high-throughput method for characterizing the motility of microorganisms in three dimensions based on standard imaging microscopy. Instead of tracking individual cells, we analyze the spatiotemporal fluctuations of the intensity in the sample from time-lapse images and obtain the intermediate scattering function of the system. We demonstrate our method on two different types of microorganisms: the bacterium Escherichia coli (both smooth swimming and wild type) and the biflagellate alga Chlamydomonas reinhardtii. We validate the methodology using computer simulations and particle tracking. From the intermediate scattering function, we are able to extract the swimming speed distribution, fraction of motile cells, and diffusivity for E. coli, and the swimming speed distribution, and amplitude and frequency of the oscillatory dynamics for C. reinhardtii. In both cases, the motility parameters were averaged over ∼ 10⁴ cells and obtained in a few minutes.     

Renewable fluid dynamic energy derived from aquatic animal locomotion

Aquatic animals swimming in isolation and in groups are known to extract energy from the vortices in environmental flows, significantly reducing muscle activity required for locomotion. A model for the vortex dynamics associated with this phenomenon is developed, showing that the energy extraction mechanism can be described by simple criteria governing the kinematics of the vortices relative to the body in the flow. In this way, we need not make direct appeal to the fluid dynamics, which can be more difficult to evaluate than the kinematics. Examples of these principles as exhibited in swimming fish and existing energy conversion devices are described. A benefit of the developed framework is that the potentially infinite-dimensional parameter space of the fluid-structure interaction is reduced to a maximum of eight combinations of three parameters. The model may potentially aid in the design and evaluation of unsteady aero- and hydrodynamic energy conversion systems that surpass the Betz efficiency limit of steady fluid dynamic energy conversion systems.