Propulsion Modeling and Analysis of a Biomimetic Swimmer

<正> We have studied a biomimetic swimmer based on the motion of bacteria such as Escherichia coli (E. coli) theoretically andexperimentally. The swimmer has an ellipsoidal cell body propelled by a helical filament. The performance of this swimmer wasestimated by modeling the dynamics of a swimmer in viscous fluid. We applied the Resistive Force Theory (RFT) on this modelto calculate the linear swimming speed and the efficiency of the model. A parametric study on linear velocity and efficiency tooptimize the design of this swimmer was demonstrated. In order to validate the theoretical results, a biomimetic swimmer wasfabricated and an experiment setup was prepared to measure the swimming speed and thrust force in silicone oil. The experimentalresults agree well with the theoretical values predicted by RFT. In addition, we studied the flow patterns surrounding thefilament with a finite element simulation with different Reynolds number (Re) to understand the mechanism of propulsion. Thesimulation results provide information on the nature of flow patterns generated by swimming filament. Furthermore, the thrustforces from the simulation were compared with the thrust forces from theory. The simulation results are in good agreement withthe theoretical results.     

Computational and mathematical modeling of the effects of tailbeat frequency and flexural stiffness in swimming fish

In this paper we describe how we combine computational and mathematical models to form virtual fish to explore different hypotheses about the impact of centra. We show how we create simulation models using a combination of a mathematical model of a fish-like robot using caudal fin propulsion, a propulsion model, and an optimizer, to explore the impact of centra under various scenarios. The optimizer uses the mathematical model to construct valid configurations of the digital robot and uses the utility function and propulsion model to evaluate the performance of each configuration. The evaluations are used to explore the adaptive landscape and find high-performing configurations. Our results show that the high-performing configurations have both increased (flexural) stiffness of the tail and higher tailbeat frequencies.     

In Silico Reconstitution of Listeria Propulsion Exhibits Nano-Saltation

To understand how the actin-polymerization-mediated movements in cells emerge from myriad individual protein–protein interactions, we developed a computational model of Listeria monocytogenes propulsion that explicitly simulates a large number of monomer-scale biochemical and mechanical interactions. The literature on actin networks and L. monocytogenes motility provides the foundation for a realistic mathematical/computer simulation, because most of the key rate constants governing actin network dynamics have been measured. We use a cluster of 80 Linux processors and our own suite of simulation and analysis software to characterize salient features of bacterial motion. Our “in silico reconstitution” produces qualitatively realistic bacterial motion with regard to speed and persistence of motion and actin tail morphology. The model also produces smaller scale emergent behavior; we demonstrate how the observed nano-saltatory motion of L. monocytogenes, in which runs punctuate pauses, can emerge from a cooperative binding and breaking of attachments between actin filaments and the bacterium. We describe our modeling methodology in detail, as it is likely to be useful for understanding any subcellular system in which the dynamics of many simple interactions lead to complex emergent behavior, e.g., lamellipodia and filopodia extension, cellular organization, and cytokinesis.     

In silico reconstitution of Listeria propulsion exhibits nano-saltation

To understand how the actin-polymerization-mediated movements in cells emerge from myriad individual protein–protein interactions, we developed a computational model of Listeria monocytogenes propulsion that explicitly simulates a large number of monomer-scale biochemical and mechanical interactions. The literature on actin networks and L. monocytogenes motility provides the foundation for a realistic mathematical/computer simulation, because most of the key rate constants governing actin network dynamics have been measured. We use a cluster of 80 Linux processors and our own suite of simulation and analysis software to characterize salient features of bacterial motion. Our “in silico reconstitution” produces qualitatively realistic bacterial motion with regard to speed and persistence of motion and actin tail morphology. The model also produces smaller scale emergent behavior; we demonstrate how the observed nano-saltatory motion of L. monocytogenes, in which runs punctuate pauses, can emerge from a cooperative binding and breaking of attachments between actin filaments and the bacterium. We describe our modeling methodology in detail, as it is likely to be useful for understanding any subcellular system in which the dynamics of many simple interactions lead to complex emergent behavior, e.g., lamellipodia and filopodia extension, cellular organization, and cytokinesis.     

Actin dynamics at sites of extracellular matrix degradation

The degradation of extracellular matrix (ECM) by proteases is crucial in physiological and pathological cell invasion alike. In vitro, degradation occurs at specific sites where invasive cells make contact with the ECM via specialized plasma membrane protrusions termed invadopodia. Here we present an extensive morpho-functional analysis of invadopodia actively engaged in ECM degradation and show that they are actin comet-based structures, not unlike the well-known bacteria-propelling actin tails. The relative mapping of the basic molecular components of invadopodia to actin tails is also provided. Finally, a live-imaging analysis of invadopodia highlights the intrinsic long-term stability of the structures coupled to a highly dynamic actin turnover. The results offer new insight into the tight coordination between signalling, actin remodelling and trafficking activities occurring at sites of focalized ECM degradation by invadopodia. In conclusion, invadopodia-associated actin comets are a striking example of consistently arising, spontaneous expression of actin-driven propulsion events that also represent a valuable experimental paradigm.     

A Prototype of a Biomimetic Mantle Jet Propeller Inspired by Cuttlefish Actuated by SMA Wires and a Theoretical Model for Its Jet Thrust

The cuttlefish have higher swimming speed and more maneuverability than most of the fish mainly benefiting from their unique jet propulsion mechanism, which is realized by the contraction and expansion of their flexible mantle. However it is difficult to mimic this jet propulsion mechanism using conventional electro-mechanical structures. In this paper, the musculature of the cuttlefish mantle and how the mantle flexibly contracts and expands were analyzed first. Then the Shape Memory Alloy（SMA） wires were chosen as the actuators and the soft silica gel was chosen as the body materials to develop a biomimetic mantle jet propeller. The SMA wires were embedded within the soft silica gel formed with cuttlefish mantle shape along the annular direction to mimic the circular muscles of cuttlefish mantle. The water was squeezed out the mantle cavity to form rear jets when the biomimetic mantle was contracted by SMA wires. A mechanical model and a thermal model were established to analyze the jet thrust and the jetting frequency. Theoretical analysis shows that the jet thrust is proportional to the square of the rate of change of SMA strain. Increasing the driving voltage can improve the rate of change of SMA strain, thus can improve both the jet thrust and the jetting frequency. However the j etting frequency is mainly restricted by the cooling of SMA wires. To maximize the jetting frequency, the optimal driving parameters for different driving voltage were calculated. The propulsion performance was tested and the results show that the jet thrust can increase with the driving voltage as predicted and the maximum average jet thrust is 0.14 N when the driving voltage is 25 V. The swimming test was carried out to verify the feasibility of the novel design. It is shown that the biomimetic jet propeller can swim with higher speed as the jet thrust and jetting frequency increase and the maximum speed can reach 8.76 cm·s^-1 （0.35 BL·s^-1） at a jetting frequency of 0.83 Hz.     

Leg stiffness increases with speed to modulate gait frequency and propulsion energy

Bipedal walking models with compliant legs have been employed to represent the ground reaction forces (GRFs) observed in human subjects. Quantification of the leg stiffness at varying gait speeds, therefore, would improve our understanding of the contributions of spring-like leg behavior to gait dynamics. In this study, we tuned a model of bipedal walking with damped compliant legs to match human GRFs at different gait speeds. Eight subjects walked at four different gait speeds, ranging from their self-selected speed to their maximum speed, in a random order. To examine the correlation between leg stiffness and the oscillatory behavior of the center of mass (CoM) during the single support phase, the damped natural frequency of the single compliant leg was compared with the duration of the single support phase. We observed that leg stiffness increased with speed and that the damping ratio was low and increased slightly with speed. The duration of the single support phase correlated well with the oscillation period of the damped complaint walking model, suggesting that CoM oscillations during single support may take advantage of resonance characteristics of the spring-like leg. The theoretical leg stiffness that maximizes the elastic energy stored in the compliant leg at the end of the single support phase is approximated by the empirical leg stiffness used to match model GRFs to human GRFs. This result implies that the CoM momentum change during the double support phase requires maximum forward propulsion and that an increase in leg stiffness with speed would beneficially increase the propulsion energy. Our results suggest that humans emulate, and may benefit from, spring-like leg mechanics.     

Geometry-Driven Polarity in Motile Amoeboid Cells

Motile eukaryotic cells, such as leukocytes, cancer cells, and amoeba, typically move inside the narrow interstitial spacings of tissue or soil. While most of our knowledge of actin-driven eukaryotic motility was obtained from cells that move on planar open surfaces, recent work has demonstrated that confinement can lead to strongly altered motile behavior. Here, we report experimental evidence that motile amoeboid cells undergo a spontaneous symmetry breaking in confined interstitial spaces. Inside narrow channels, the cells switch to a highly persistent, unidirectional mode of motion, moving at a constant speed along the channel. They remain in contact with the two opposing channel side walls and alternate protrusions of their leading edge near each wall. Their actin cytoskeleton exhibits a characteristic arrangement that is dominated by dense, stationary actin foci at the side walls, in conjunction with less dense dynamic regions at the leading edge. Our experimental findings can be explained based on an excitable network model that accounts for the confinement-induced symmetry breaking and correctly recovers the spatio-temporal pattern of protrusions at the leading edge. Since motile cells typically live in the narrow interstitial spacings of tissue or soil, we expect that the geometry-driven polarity we report here plays an important role for movement of cells in their natural environment.     

How does stochasticity in colonization accelerate the speed of invasion in a cellular automaton model?

We investigate the speed of invasion waves for a single species generated by stochastic short- and/or long-distance colonizations in a time-continuous cellular automaton (CA) model on a two-dimensional homogenous landscape. By simulating the CA models, we demonstrate that stochasticity can dramatically increase the speed of invasion compared to the corresponding deterministic CA model or the corresponding one-dimensional stochastic CA model. To explain this phenomenon, we first develop a mathematical model for the invasion involving only short-distance colonization (i.e., colonization only occurs from the eight adjacent cells), and present several approximation methods for solving the model. Our analyses show that the increased wave speed in the stochastic model is due to irregularity in the shape of the wavefront. Further extension of this model to include long-distance colonization demonstrates that stochasticity influences speeds to even greater extents in this case. Using dimension analysis, we deduced a semi-empirical formula for the speed as a function of three parameters intrinsic to short- and long-distance colonization, which agrees well with simulation results. Based on these results, we discuss how important stochasticity in colonization and spatial dimensionality are in the acceleration of invasion speed.     

Estimation of the potential speed of range expansion of an introduced species: characteristics and applicability of the gamma model

The potential speed at which the range of an introduced species expands in its optimal environment can be predicted by using the gamma model proposed by Yamamura (Popul Ecol 46:87–101, 2004). In this paper we first clarify the difference between the gamma model and Einstein’s Brownian motion model. We then apply the model to the ragweed beetle, Ophraella communa LeSage that rapidly expanded its distribution in Japan after it was first found in 1996. The parameters of the model are estimated by conducting a field experiment. The species’ net reproductive rate is examined in the laboratory. By combining these estimates, we estimate the potential speed of range expansion to be 82 km per generation and 329 km per year, while the observed speed is estimated to be 77 km per year, the observed speed being considerably slower than the potential speed. This discrepancy may be due to the low reproductive rate caused by mortality in the actual field. The applicability of the gamma model to the econometric data is also briefly discussed.     

A mathematical explanation of an increase in bacterial swimming speed with viscosity in linear-polymer solutions

Bacterial swimming speed is sometimes known to increase with viscosity. This phenomenon is peculiar to bacterial motion. Berg and Turner (Nature. 278:349-351, 1979) indicated that the phenomenon was caused by a loose, quasi-rigid network formed by polymer molecules that were added to increase viscosity. We mathematically developed their concept by introducing two apparent viscosities and obtained results similar to the experimental data reported before. Addition of polymer improved the propulsion efficiency, which surpasses the decline in flagellar rotation rate, and the swimming speed increased with viscosity.     

Dynamic Modeling, Testing, and Stability Analysis of an Ornithoptic Blimp

In order to study omithopter flight and to improve a dynamic model of flapping propulsion,a series of tests are conducted on a flapping-wing blimp.The blimp is designed and constructed from mylar plastic and balsa wood as a test platform for aerodynamics and flight dynamics.The blimp,2.3 meters long and 420 gram mass,is propelled by its flapping wings.Due to buoyancy the wings have no lift requirement so that the distinction between lift and propulsion can be analyzed in a flight platform at low flight speeds.The blimp is tested using a Vicon motion tracking system and various initial conditions are tested including accelerating flight from standstill,decelerating from an initial speed higher than its steady state,and from its steady-state speed but disturbed in pitch angle.Test results are used to estimate parameters in a coupled quasi-steady aerodynamics/Newtonian flight dynamics model.This model is then analyzed using Floquet theory to determine local dynamic modes and stability.It is concluded that the dynamic model adequately describes the vehicle's nonlinear behavior near the steady-state velocity and that the vehicle's linearized modes are akin to those of a fixed-wing aircraft.     

Body Fineness Ratio as a Predictor of Maximum Prolonged-Swimming Speed in Coral Reef Fishes

The ability to sustain high swimming speeds is believed to be an important factor affecting resource acquisition in fishes. While we have gained insights into how fin morphology and motion influences swimming performance in coral reef fishes, the role of other traits, such as body shape, remains poorly understood. We explore the ability of two mechanistic models of the causal relationship between body fineness ratio and endurance swimming-performance to predict maximum prolonged-swimming speed (U_max) among 84 fish species from the Great Barrier Reef, Australia. A drag model, based on semi-empirical data on the drag of rigid, submerged bodies of revolution, was applied to species that employ pectoral-fin propulsion with a rigid body at U _max. An alternative model, based on the results of computer simulations of optimal shape in self-propelled undulating bodies, was applied to the species that swim by body-caudal-fin propulsion at U_max. For pectoral-fin swimmers, U_max increased with fineness, and the rate of increase decreased with fineness, as predicted by the drag model. While the mechanistic and statistical models of the relationship between fineness and U_max were very similar, the mechanistic (and statistical) model explained only a small fraction of the variance in U_max. For body-caudal-fin swimmers, we found a non-linear relationship between fineness and U_max, which was largely negative over most of the range of fineness. This pattern fails to support either predictions from the computational models or standard functional interpretations of body shape variation in fishes. Our results suggest that the widespread hypothesis that a more optimal fineness increases endurance-swimming performance via reduced drag should be limited to fishes that swim with rigid bodies.     

Propulsive adaptation to changing gait speed

Understanding propulsion and adaptation to speed requirements is important in determining appropriate therapies for gait disorders. We hypothesize that adaptations for changing speed requirements occur primarily at the hip. The slow, normal and fast gait of 24 healthy young subjects was analyzed. The linear power was analyzed at the hip joint. The anterior-posterior and vertical induced accelerations of the hip were also determined. Linear power and anterior-posterior-induced acceleration (IA) analyses of the hip reveal that the lower limb joint's moments contribute to body forward propulsion primarily during late swing and early stance. Propulsive adaptations to speed changes occur primarily at the hip and secondarily at the ankle. These analyses show that hip muscles, particularly the hip extensors, are critical to propulsion. They also show that ankle function is primarily for support, but is important to propulsion, especially at slow speeds.     

Swimming Behavior Analysis Based on Bacterial Chemotaxis in Solution

Microrobots is playing more and more important roles for medical applications,such as targeting tumoral lesions for therapeutic purposes,Minimally Invasive Surgery (MIS) and highly localized drug delivery.However,energy efficient propulsion system poses significant challenges for the implementation of such mobile robots.Flagellated chemotactic bacteria can be used as an effective integrated propulsion system for microrobots.In this paper,we proposed a new type of propulsion method that is inspired by the motility mechanism of flagellated chemotactic bacteria in different pH gradients.The pH gradient field was established in solution through electrolysis method.The distribution of the pH values in solution was measured with pH indicator and analyzed with image processing technology,and the mechanism by which the pH values changed was also discussed.The swimming speed and direction of the bacteria were studied experimentally.Through analyzing the key parameters,such as stabilization time and electrode voltage,the optimal design of propulsion mechanism based on bacteria motion in the pH gradient field was proven.     

Validated biomechanical model for efficiency and speed of rowing

The speed of a competitive rowing crew depends on the number of crew members, their body mass, sex and the type of rowing—sweep rowing or sculling. The time-averaged speed is proportional to the rower?s body mass to the 1/36^th power, to the number of crew members to the1/9^th power and to the physiological efficiency (accounted for by the rower?s sex) to the 1/3^rd power. The quality of the rowing shell and propulsion system is captured by one dimensionless parameter that takes the mechanical efficiency, the shape and drag coefficient of the shell and the Froude propulsion efficiency into account. We derive the biomechanical equation for the speed of rowing by two independent methods and further validate it by successfully predicting race times. We derive the theoretical upper limit of the Froude propulsion efficiency for low viscous flows. This upper limit is shown to be a function solely of the velocity ratio of blade to boat speed (i.e., it is completely independent of the blade shape), a result that may also be of interest for other repetitive propulsion systems.     

Modelling actin polymerization: the effect on confined cell migration

The aim of this work is to model cell motility under conditions of mechanical confinement. This cell migration mode may occur in extravasation of tumour and neutrophil-like cells. Cell migration is the result of the complex action of different forces exerted by the interplay between myosin contractility forces and actin processes. Here, we propose and implement a finite element model of the confined migration of a single cell. In this model, we consider the effects of actin and myosin in cell motility. Both filament and globular actin are modelled. We model the cell considering cytoplasm and nucleus with different mechanical properties. The migration speed in the simulation is around 0.1 μm/min, which is in agreement with existing literature. From our simulation, we observe that the nucleus size has an important role in cell migration inside the channel. In the simulation the cell moves further when the nucleus is smaller. However, this speed is less sensitive to nucleus stiffness. The results show that the cell displacement is lower when the nucleus is stiffer. The degree of adhesion between the channel walls and the cell is also very important in confined migration. We observe an increment of cell velocity when the friction coefficient is higher.

     

Direct Measurement of Helical Cell Motion of the Spirochete Leptospira

Leptospira are spirochete bacteria distinguished by a short-pitch coiled body and intracellular flagella. Leptospira cells swim in liquid with an asymmetric morphology of the cell body; the anterior end has a long-pitch spiral shape (S-end) and the posterior end is hook-shaped (H-end). Although the S-end and the coiled cell body called the protoplasmic cylinder are thought to be responsible for propulsion together, most observations on the motion mechanism have remained qualitative. In this study, we analyzed the swimming speed and rotation rate of the S-end, protoplasmic cylinder, and H-end of individual Leptospira cells by one-sided dark-field microscopy. At various viscosities of media containing different concentrations of Ficoll, the rotation rate of the S-end and protoplasmic cylinder showed a clear correlation with the swimming speed, suggesting that these two helical parts play a central role in the motion of Leptospira. In contrast, the H-end rotation rate was unstable and showed much less correlation with the swimming speed. Forces produced by the rotation of the S-end and protoplasmic cylinder showed that these two helical parts contribute to propulsion at nearly equal magnitude. Torque generated by each part, also obtained from experimental motion parameters, indicated that the flagellar motor can generate torque >4000 pN nm, twice as large as that of Escherichia coli. Furthermore, the S-end torque was found to show a markedly larger fluctuation than the protoplasmic cylinder torque, suggesting that the unstable H-end rotation might be mechanically related to changes in the S-end rotation rate for torque balance of the entire cell. Variations in torque at the anterior and posterior ends of the Leptospira cell body could be transmitted from one end to the other through the cell body to coordinate the morphological transformations of the two ends for a rapid change in the swimming direction.