Swimming Strategies Research Articles

Run-and-tumble bacteria slowly approaching the diffusive regime.

The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a dilute swimmer suspension to reach the diffusive regime as well as what is the amplitude of the deviations from the diffusive dynamics. A linear time dependence of the mean-squared displacement (MSD) is insufficient to characterize diffusion and thus we also focus on the excess kurtosis of the displacement distribution. Four swimming strategies are considered: (i) the conventional RT model with complete reorientation after tumbling; (ii) the case of partial reorientation, characterized by a distribution of tumbling angles; (iii) a run-and-reverse model with rotational diffusion; and (iv) a RT particle where the tumbling rate depends on the stochastic concentration of an internal protein. By analyzing the associated kinetic equations for the probability density function and simulating the models, we find that for models (ii), (iii), and (iv) the relaxation to diffusion can take much longer than the mean time between tumble events, evidencing the existence of large tails in the particle displacements. Moreover, the excess kurtosis can assume large positive values. In model (ii) it is possible for some distributions of tumbling angles that the MSD reaches a linear time dependence but, still, the dynamics remains non-Gaussian for long times. This is also the case in model (iii) for small rotational diffusivity. For all models, the long-time diffusion coefficients are also obtained. The theoretical approach, which relies on eigenvalue and angular Fourier expansions of the van Hove function, is in excellent agreement with the simulations.

Magnetically powered metachronal waves induce locomotion in self-assemblies

When tiny soft ferromagnetic particles are placed along a liquid interface and exposed to a vertical magnetic field, the balance between capillary attraction and magnetic repulsion leads to self-organization into well-defined patterns. Here, we demonstrate experimentally that precessing magnetic fields induce metachronal waves on the periphery of these assemblies, similar to the ones observed in ciliates and some arthropods. The outermost layer of particles behaves like an array of cilia or legs whose sequential movement causes a net and controllable locomotion. This bioinspired many-particle swimming strategy is effective even at low Reynolds number, using only spatially uniform fields to generate the waves.

A transition to stable one-dimensional swimming enhances E. coli motility through narrow channels

Living organisms often display adaptive strategies that allow them to move efficiently even in strong confinement. With one single degree of freedom, the angle of a rotating bundle of flagella, bacteria provide one of the simplest examples of locomotion in the living world. Here we show that a purely physical mechanism, depending on a hydrodynamic stability condition, is responsible for a confinement induced transition between two swimming states in E. coli. While in large channels bacteria always crash onto confining walls, when the cross section falls below a threshold, they leave the walls to move swiftly on a stable swimming trajectory along the channel axis. We investigate this phenomenon for individual cells that are guided through a sequence of micro-fabricated tunnels of decreasing cross section. Our results challenge current theoretical predictions and suggest effective design principles for microrobots by showing that motility based on helical propellers provides a robust swimming strategy for exploring narrow spaces.

Optimal actuation of flagellar magnetic microswimmers.

We present an automated procedure for the design of optimal actuation for flagellar magnetic microswimmers based on numerical optimization. Using this method, a magnetic actuation method is provided which allows these devices to swim significantly faster compared to the usual sinusoidal actuation. This leads to a novel swimming strategy which makes the swimmer perform a three-dimensional figure-eight trajectory. This shows that a faster propulsion is obtained when the swimmer is allowed to go out of plane. This approach is experimentally validated on a scaled-up flexible swimmer.

Swimming strategy of settling elongated micro-swimmers by reinforcement learning

Particular types of plankton in aquatic ecosystems can coordinate their motion depending on the local flow environment to reach regions conducive to their growth or reproduction. Investigating their swimming strategies with regard to the local environment is important to obtain in-depth understanding of their behavior in the aquatic environment. In the present research, to examine an impact of the shape and gravity on a swimming strategy, plankton is considered as settling swimming particles of ellipsoidal shape. The Q-learning approach is adopted to obtain swimming strategies for smart particles with a goal of efficiently moving upwards in a two-dimensional steady flow. Strategies obtained from reinforcement learning are compared to those of naive gyrotactic particles that is modeled considering the behavior of realistic plankton. It is found that elongation of particles improves the performance of upward swimming by facilitating particles' resistance to the perturbation of vortex. In the case when the settling velocity is included, the strategy obtained by reinforcement learning has similar performance to that of the naive gyrotactic one, and they both align swimmers in upward direction. The similarity between the strategy obtained from machine learning and the biological gyrotactic strategy indicates the relationship between the aspherical shape and settling effect of realistic plankton and their gyrotactic feature.

Dynamics of a spherical droplet driven by active slip and stress

We study low Reynolds number locomotion of a spherical viscous droplet, in an unbounded arbitrary Stokes flow, under the combined influence of an inhomogeneous surfactant (diffusiophoresis) and non-isothermal temperature (Marangoni effect) fields. The self-generated gradient of the surfactant concentration and the influence of the external temperature field are respectively mapped as a slip velocity and stress discontinuity across the surface of the droplet. The drag force exerted on the droplet is computed in the form of Faxen’s laws. As a particular case, droplet migrating in a Poiseuille flow has been discussed. Depending on the directions of the induced slip and stress fields, with respect to the Poiseuille flow, the intermediate competitive behavior is highlighted by analyzing the migration velocity, power dissipation and the swimming pattern of the droplet. We have observed that the external stress inverts both the direction of migration velocity as well as the nature of swimming, i.e., turns a pusher into a puller and vice versa, induced by the active slip of the swimmer. Correspondingly, a set of critical points for the velocity reversal and the swimming pattern transition are obtained. Interestingly, the swimmer dissipates minimum power during the transitions. Finally, the present model can draw a striking analogy with the behavior of the microorganisms in an active stress environment, where the intrinsic slip velocity of the microorganisms and the external stress effects are self-reliant and expected to influence the swimming strategies significantly. The obtained analytical results corroborate with the existing literature in suitable limits, which show the accuracy and validity of the solutions.

Modelling the ingress of a temperate fish larva into a nursery coastal lagoon

The development of sensorial acuity and swimming capabilities of coastal fish larvae and their responses to coastal nursery cues are essential for recruitment success. Most studies of the response of fish larvae to environmental cues and their recruitment into nursery areas have focused on coral reef fish and only a few studies focused on fish species from temperate regions. The Sense Acuity and Behavioural (SAAB) Hypothesis proposes that fish larvae in temperate regions can sense nursery cues and ingress into estuarine ecosystems by using several active swimming strategies. We tested the SAAB hypothesis by studying the ingress of a temperate fish larvae – white seabream Diplodus sargus (Linnaeus, 1758) – into a coastal nursery area, the Ria Formosa Lagoon, Portugal. We combined the results from studies of sensory acuity, swimming capabilities and personality traits of post-flexion larvae with a fine-scale biophysical model to quantify the ingress of the white seabream into the lagoon. Data showed that the location of spawning sites and the directional swimming capabilities are both important for the successful ingress of white seabream larvae into the lagoon. Recruitment was higher when spawning grounds were located in areas with depths between 15.1 and 16.9 m and when post-flexion larvae used their directional swimming capabilities. The larvae ingressed passively into the lagoon with the tidal currents at pre-flexion stage and actively by using their directional swimming capabilities at post-flexion stage. Directional swimming also prevented larval export into the coastal area. When spawning occurred away from the seagrass smell plume emanating from the lagoon, the fish larvae were advected away and lost at sea. This work demonstrated the relevance of combining fish larvae behaviour and oceanography processes in modelling the dispersion of fish larvae to estimate recruitment.

Jellyfish-Inspired Soft Robot Driven by Fluid Electrode Dielectric Organic Robotic Actuators.

Robots for underwater exploration are typically comprised of rigid materials and driven by propellers or jet thrusters, which consume a significant amount of power. Large power consumption necessitates a sizeable battery, which limits the ability to design a small robot. Propellers and jet thrusters generate considerable noise and vibration, which is counterproductive when studying acoustic signals or studying timid species. Bioinspired soft robots provide an approach for underwater exploration in which the robots are comprised of compliant materials that can better adapt to uncertain environments and take advantage of design elements that have been optimized in nature. In previous work, we demonstrated that frameless DEAs could use fluid electrodes to apply a voltage to the film and that effective locomotion in an eel-inspired robot could be achieved without the need for a rigid frame. However, the robot required an off-board power supply and a non-trivial control signal to achieve propulsion. To develop an untethered soft swimming robot powered by DEAs, we drew inspiration from the jellyfish and attached a ring of frameless DEAs to an inextensible layer to generate a unimorph structure that curves toward the passive side to generate power stroke, and efficiently recovers the original configuration as the robot coasts. This swimming strategy simplified the control system and allowed us to develop a soft robot capable of untethered swimming at an average speed of 3.2 mm/s and a cost of transport of 35. This work demonstrates the feasibility of using DEAs with fluid electrodes for low power, silent operation in underwater environments.

Photocatalytic BiVO4 Microswimmers with Bimodal Swimming Strategies

Photocatalytic micromotors are developing rapidly and environmental applications seem very promising and within reach. However, the complex synthesis strategies, jointly with the large band gaps of most efficient swimmers inhibit both, applications and upscaling. Herein, a simple solvothermal synthesis of well defined, catalytically active BiVO4 microparticles, which can propel efficiently without asymmetrization is presented. Those microparticles respond to blue and UV light and are able to switch between different motion strategies, similar to bacterial microswimmers. These behavioral changes are controlled by changing the pH value of the environment.

Thrust and Power Output of the Bacterial Flagellar Motor: A Micromagnetic Tweezers Approach

One of the most common swimming strategies employed by microorganisms is based on the use of rotating helical filaments, called flagella, that are powered by molecular motors. Determining the physical properties of this propulsive system is crucial to understanding the behavior of these organisms. Furthermore, the ability to dynamically monitor the activity of the flagellar motor is a valuable indicator of the overall energetics of the cell. In this work, inherently magnetic bacteria confined in micromagnetic CoFe traps are used to directly and noninvasively determine the flagellar thrust force and swimming speed of motile cells. The technique permits determination of the ratio of propulsive force/swimming speed (the hydrodynamic resistance) and the power output of the flagellar motor for individual cells over extended time periods. Cells subjected to ultraviolet radiation are observed to experience exponential decays in power output as a function of exposure time. By noninvasively measuring thrust, velocity, and power output over time at a single-cell level, this technique can serve as the foundation for fundamental studies of bacterial hydrodynamics and also provides a novel, to our knowledge, tether-free probe of single-cell energetics over time.

Hydrodynamic and biological constraints on group cohesion in plankton

The dynamics of plankton in the ocean are determined by biophysical interactions. Although physics and biotic behaviors are known to influence the observed patchiness of planktonic populations, it is still unclear how much, and if, group behavior contributes to this biophysical interaction. Here, we demonstrate how simple rules of behavior can enhance or inhibit active group cohesion in plankton in a turbulent environment. In this study, we used coral-reef fish larvae as a model to investigate the interaction between microscale turbulence and planktonic organisms. We synthesized available information on the swimming speeds and sizes of reef fish larvae, and developed a set of equations to investigate the effects of viscosity and turbulence on larvae dispersion. We then calculated the critical dispersion rates for three different swimming strategies – cruise, random-walk, and pause-travel – to determine which strategies could facilitate group cohesion during dispersal. Our results indicate that swimming strategies and migration to low-turbulence regions are the key to maintaining group cohesion, suggesting that many reef fish species have the potential to remain together, from hatching to settlement. In addition, larvae might change their swimming strategies to maintain group cohesion, depending on environmental conditions and/or their ontogenic stage. This study provides a better understanding of the hydrodynamic and biological constraints on group formation and cohesion in planktonic organisms, and reveals a wide range of conditions under which group formation may occur.

Swimming eukaryotic microorganisms exhibit a universal speed distribution.

One approach to quantifying biological diversity consists of characterizing the statistical distribution of specific properties of a taxonomic group or habitat. Microorganisms living in fluid environments, and for whom motility is key, exploit propulsion resulting from a rich variety of shapes, forms, and swimming strategies. Here, we explore the variability of swimming speed for unicellular eukaryotes based on published data. The data naturally partitions into that from flagellates (with a small number of flagella) and from ciliates (with tens or more). Despite the morphological and size differences between these groups, each of the two probability distributions of swimming speed are accurately represented by log-normal distributions, with good agreement holding even to fourth moments. Scaling of the distributions by a characteristic speed for each data set leads to a collapse onto an apparently universal distribution. These results suggest a universal way for ecological niches to be populated by abundant microorganisms.

Impact of hormone-therapy used in CRPC patients: Evaluation of abiraterone acetate/prednisone or enzalutamide on activity and cognitive functions in aged castrated mice.

e16526 Background: Prostate cancer (PC) is a major public health problem and represents the most frequent cancer in elderly male patients. Although most patients initially respond to androgen deprivation therapy (ADT) through inhibition of gonadal testosterone biosynthesis, the majority of these patients will progress to metastatic castration-resistant PC (mCRPC). Novel oral agents targeting androgen signaling axis, abiraterone acetate (AA)+prednisone (P) and enzalutamide (ENZ) are available and used in mCRPC patients in addition to ADT, but their impact on cognition is not well understood. Recently, the AQUARiUS study (Thiery-Vuillemin et al., ESMO Open, 2018) showed that after treatment, median Quality of life score improved with AAP. Additionally, results from a phase 2 trial showed that a worsening of depression symptoms were more often detected in ENZ- than in AAP-treated patients (Khalaf et al., Eur Urol, 2018). Methods: Here we developed a preclinical animal model to clarify the potential impact of AAP or ENZ on emotional reactivity and cognitive functions including spontaneous activity, anxiety-like and depression-like behaviors or spatial memory and learning. Results: In aged castrated mice receiving per os vehicle or AAP or ENZ, we showed that, in contrast to AAP, exposure to ENZ reduced spontaneous activity and increased depressive-like behaviors. AAP-treated mice displayed diminished self-grooming suggesting lower arousal in a novel environment. None of the treatments provoked anxiety-like behavior, learning and memory deficits. However, the swimming strategies (Morris-water maze) in AAP and ENZ groups were slightly altered. Analysis of plasma from treated mice revealed a detectable level of corticosterone only in AAP group. Conclusions: These data establish the impact of ENZ on emotional reactivity and of both ENZ and AAP on subtle cognitive functions in castrated aged male subjects. It paves the road for future effective research that could lead to better management of quality of life in mCRPC.

Assessing the Influence of Personality on Sensitivity to Magnetic Fields in Zebrafish.

To orient themselves in their environment, animals integrate a wide array of external cues, which interact with several internal factors, such as personality. Here, we describe a behavioral protocol designed for the study of the influence of zebrafish personality on their orientation response to multiple external environmental cues, specifically water currents and magnetic fields. This protocol aims to understand whether proactive or reactive zebrafish display different rheotactic thresholds (i.e., the flow speed at which the fish start swimming upstream) when the surrounding magnetic field changes its direction. To identify zebrafish with the same personality, fish are introduced in the dark half of a tank connected with a narrow opening to a bright half. Only proactive fish explore the novel, bright environment. Reactive fish do not exit the dark half of the tank. A swimming tunnel with low flow rates is used to determine the rheotactic threshold. We describe two setups to control the magnetic field in the tunnel, in the range of the earth's magnetic field intensity: one that controls the magnetic field along the flow direction (one dimension) and one that allows a three-axial control of the magnetic field. Fish are filmed while experiencing a stepwise increase of the flow speed in the tunnel under different magnetic fields. Data on the orientation behavior are collected through a video-tracking procedure and applied to a logistic model to allow the determination of the rheotactic threshold. We report representative results collected from shoaling zebrafish. Specifically, these demonstrate that only reactive, prudent fish show variations of the rheotactic threshold when the magnetic field varies in its direction, while proactive fish do not respond to magnetic field changes. This methodology can be applied to the study of magnetic sensitivity and rheotactic behavior of many aquatic species, both displaying solitary or shoaling swimming strategies.

Swimming strategies and energetics of endothermic white sharks during foraging.

Some fishes and sea turtles are distinct from ectotherms by having elevated core body temperatures and metabolic rates. Quantifying the energetics and activity of the regionally endothermic species will help us understand how a fundamental biophysical process (i.e. temperature-dependent metabolism) shapes animal ecology; however, such information is limited owing to difficulties in studying these large, highly active animals. White sharks, Carcharodon carcharias, are the largest fish with regional endothermy, and potentially among the most energy-demanding fishes. Here, we deployed multi-sensor loggers on eight white sharks aggregating near colonies of long-nosed fur seals, Arctocephalus forsteri, off the Neptune Islands, Australia. Simultaneous measurements of depth, swim speed (a proxy for swimming metabolic rate) and body acceleration (indicating when sharks exhibited energy-efficient gliding behaviour) revealed their fine-scale swimming behaviour and allowed us to estimate their energy expenditure. Sharks repeatedly dived (mean swimming depth, 29 m) and swam at the surface between deep dives (maximum depth, 108 m). Modal swim speeds (0.80-1.35 m s-1) were slower than the estimated speeds that minimize cost of transport (1.3-1.9 m s-1), a pattern analogous to a 'sit-and-wait' strategy for a perpetually swimming species. All but one shark employed unpowered gliding during descents, rendering deep (>50 m) dives 29% less costly than surface swimming, which may incur additional wave drag. We suggest that these behavioural strategies may help sharks to maximize net energy gains by reducing swimming cost while increasing encounter rates with fast-swimming seals.

An Automated Water Task to Test Visual Discrimination Performance, Adaptive Strategies and Stereotyped Choices in Freely Moving Mice.

We describe an automated training/testing system for adult mice that allows reliable quantification of visual discrimination capacities, adaptive swimming strategies, and stereotyped choices with minimal human intervention. The experimental apparatus consists of a hexagonal swimming pool with an internal decision zone leading to three interior arms with two software-controlled platforms inside of each arm. Each experimental trial consists in projecting a “positive” conditioned discriminative stimulus (SD) in one randomly chosen arm, whereas the other two arms project non-reinforced stimuli (the delta stimuli, SΔ). By employing a classical behavioral training schedule, the mice learn to swim toward the arm that displays the SD, because it predicts the presence of two elevated platforms located symmetrically to the left and right side of the projecting monitor. Separate behavioral components for discriminative and stereotyped choice behavior can be identified through this geometric arrangement. In addition, the projection in real-time of either static or dynamic visual stimuli allows the usage of training programs contingent on current behavioral performance. We validated the system by characterizing the visual acuity and contrast sensitivities in a group of trained mice. By employing pharmacological manipulations, we found that the mice required an intact functioning of the primary visual cortex (V1) to solve the hexagonal pool. Overall, the automated training system constitutes a reliable, rapid, and inexpensive method to quantify visual capacities of mice. It can be used to characterize visual and non-visual factors of choice behavior. It can also be combined with manipulations of visual experience and pharmacological micro-infusions to investigate integrated brain function and learning processes in adult mice over consecutive days.

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.

Study of Atlantic salmon post-smolt movement in the Gulf of St. Lawrence using an individual-based model

This study examines the effect of environmental conditions and swimming behaviors on the movement of Atlantic salmon (Salmo salar) post-smolts (juveniles) in the Gulf of St. Lawrence (GSL) using an individual-based model (IBM). The IBM uses time-varying and three-dimensional currents and hydrography produced by an ocean circulation model combined with a numerical particle-tracking scheme where swimming behaviors can be specified. Various experiments are run using this IBM with the aim of gaining insight into the observed movements of post-smolts documented in a past field study. In that study, a post-smolt released from the Saint-Jean River on the north shore of the GSL in June 2010 was found to exit the GSL through the Strait of Belle Isle (SBI) to the northeast of the release area. Two other post-smolts, released later in June 2010, were detected near Anticosti Island (AI) to the southwest of the release area. The numerical results suggest that, for both the post-smolt(s) that moved to the SBI and towards AI, the ambient near-surface circulation patterns favored their movements. In the case of movement towards AI, the travel times simulated using the simulated circulation pattern and a variety of swimming behaviors agree well with observations. For movement towards the SBI, an efficient swimming strategy is necessary in addition to a favorable circulation pattern in order for simulated travel times to be similar to observations. This study suggests two successful strategies for movement towards the SBI: (a) swimming with currents in favorable directions and against currents in unfavorable directions, and (b) swimming towards a series of target locations that define a migration route. The possibility that Atlantic salmon post-smolts originating from rivers on the north shore of the GSL may sometimes be confined to the GSL instead of migrating to the open ocean is consistent with past observational studies.

Magnetic Biohybrid Vesicles Transported by an Internal Propulsion Mechanism.

Some biological microorganisms can crawl or swim due to coordinated motions of their cytoskeleton or the flagella located inside their bodies, which push the cells forward through intracellular forces. To date, there is no demonstration of synthetic systems propelling at low Reynolds number via the precise actuation of the material confined within an enclosing lipid membrane. Here, we report lipid vesicles and other more complex self-assembled biohybrid structures able to propel due to the advection flows generated by the actuated rotation of the superparamagnetic particles they contain. The proposed swimming and release strategies, based on cooperative hydrodynamic mechanisms and near-infrared laser pulse-triggered destabilization of the phospholipid membranes, open new possibilities for the on-command transport of minute quantities of drugs, fluidor nano-objects. The lipid membranes protect the confined substances from the outside environment during transportation, thus enabling them to work in physiological conditions.

Kinematic study on a self-propelled bionic underwater robot with undulation and jet propulsion modes

SUMMARYThis paper proposed a novel type of bionic underwater robot (BUR). The undulation and jet propulsion modes on the self-propelled BUR were combined, and the kinematic characteristics of the two propulsion modes were thoroughly compared. First, the prototype and swimming strategy of the BUR were presented, and a dynamic model of the BUR was established based on several assumptions. Then, a central pattern generator (CPG) model allowing free adjustment of frequency and amplitude was employed to achieve the undulation propulsion of carangiform fish and the jet propulsion of jellyfish. Also, the kinematic characteristics of the two propulsion modes were investigated through experiments under different caudal fin actuation parameters. The experimental results indicate that the developed prototype can realize the undulation and jet propulsion by the means of the coordinated movement of the multi-caudal fins. By adjusting the CPG parameters, the BUR can switch the propulsion mode smoothly. Furthermore, the propulsion velocity of the BUR initially increased rapidly with the frequency and then slowed down when the frequency was greater than 0.8 Hz in both propulsion modes. The undulation propulsion velocity increased with the amplitude in the measurement ranges, however, the jet propulsion velocity initially increased quickly with the amplitude and then kept constant and even decreased when the amplitude was greater than 11 cm. Under the same caudal fin actuation parameters, the average velocity in undulation propulsion mode was higher than that in jet propulsion mode.