Shape of optimal active flagella

Many eukaryotic cells use the active waving motion of flexible flagella to self-propel in viscous fluids. However, the criteria governing the selection of particular flagellar waveforms among all possible shapes has proved elusive so far. To address this question, we derive computationally the optimal shape of an internally-forced periodic planar flagellum deforming as a travelling wave. The optimum is here defined as the shape leading to a given swimming speed with minimum energetic cost. To calculate the energetic cost though, we consider the irreversible internal power expanded by the molecular motors forcing the flagellum, only a portion of which ending up dissipated in the fluid. This optimisation approach allows us to derive a family of shapes depending on a single dimensionless number quantifying the relative importance of elastic to viscous effects: the Sperm number. The computed optimal shapes are found to agree with the waveforms observed on spermatozoon of marine organisms, thus suggesting that these eukaryotic flagella might have evolved to be mechanically optimal.Comment: 10 pages, 5 figure

Simulation-based analysis of micro-robots swimming at the center and near the wall of circular mini-channels

Swimming micro robots have great potential in biomedical applications such as targeted drug delivery, medical diagnosis, and destroying blood clots in arteries. Inspired by swimming micro organisms, micro robots can move in biofluids with helical tails attached to their bodies. In order to design and navigate micro robots, hydrodynamic characteristics of the flow field must be understood well. This work presents computational fluid dynamics (CFD) modeling and analysis of the flow due to the motion of micro robots that consist of magnetic heads and helical tails inside fluid-filled channels akin to bodily conduits; special emphasis is on the effects of the radial position of the robot. Time-averaged velocities, forces, torques, and efficiency of the micro robots placed in the channels are analyzed as functions of rotation frequency, helical pitch (wavelength) and helical radius (amplitude) of the tail. Results indicate that robots move faster and more efficiently near the wall than at the center of the channel. Forces acting on micro robots are asymmetrical due to the chirality of the robot’s tail and its motion. Moreover, robots placed near the wall have a different flow pattern around the head when compared to in-center and unbounded swimmers. According to simulation results, time-averaged for-ward velocity of the robot agrees well with the experimental values measured previously for a robot with almost the same dimensions

Physics of Microswimmers - Single Particle Motion and Collective Behavior

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics (to appear

The hydrodynamics of swimming microorganisms

Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection, and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming (tens of microns and below). The focus is on the fundamental flow physics phenomena occurring in this inertia-less realm, and the emphasis is on the simple physical picture. We review the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming, such as resistance matrices for solid bodies, flow singularities, and kinematic requirements for net translation. Then we review classical theoretical work on cell motility: early calculations of the speed of a swimmer with prescribed stroke, and the application of resistive-force theory and slender-body theory to flagellar locomotion. After reviewing the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of small-scale artificial swimmers, and the optimization of locomotion strategies.Comment: Review articl

Bio-inspired micro robots swimming in channels

Swimming micro robots that mimic micro organisms have a huge potential in biomedical applications such as opening clogged hard-to-reach arteries, targeted drug delivery and diagnostic operations. Typically, a micro swimmer that consists of a magnetic bead as its body, which is attached to a rigid helical tail, is actuated by a rotating external magnetic field and moved forward in the direction of the rotation in fluids. Understanding of hydrodynamic effects has utmost importance for modeling and prediction of the trajectory of the robot. In this work, a computational fluid dynamics (CFD) model is presented for the mm-long swimmer with the helical tail; the swimmer is used in our previous experiments on the effect of the confinement of the robot in a liquid filled channel. Forward velocity, fluid forces and torques on the micro swimmer are studied with respect to robot’s radial position in the channel and the number of waves on the helical tail. Forward velocities from the CFD model for the robots swimming near the wall agree reasonably well with experimental measurements

Human sperm accumulation near surfaces: a simulation study

A hybrid boundary integral/slender body algorithm for modelling flagellar cell motility is presented. The algorithm uses the boundary element method to represent the ‘wedge-shaped’ head of the human sperm cell and a slender body theory representation of the flagellum. The head morphology is specified carefully due to its significant effect on the force and torque balance and hence movement of the free-swimming cell. The technique is used to investigate the mechanisms for the accumulation of human spermatozoa near surfaces. Sperm swimming in an infinite fluid, and near a plane boundary, with prescribed planar and three-dimensional flagellar waveforms are simulated. Both planar and ‘elliptical helicoid’ beating cells are predicted to accumulate at distances of approximately 8.5–22 μm from surfaces, for flagellar beating with angular wavenumber of 3π to 4π. Planar beating cells with wavenumber of approximately 2.4π or greater are predicted to accumulate at a finite distance, while cells with wavenumber of approximately 2π or less are predicted to escape from the surface, likely due to the breakdown of the stable swimming configuration. In the stable swimming trajectory the cell has a small angle of inclination away from the surface, no greater than approximately 0.5°. The trapping effect need not depend on specialized non-planar components of the flagellar beat but rather is a consequence of force and torque balance and the physical effect of the image systems in a no-slip plane boundary. The effect is relatively weak, so that a cell initially one body length from the surface and inclined at an angle of 4°–6° towards the surface will not be trapped but will rather be deflected from the surface. Cells performing rolling motility, where the flagellum sweeps out a ‘conical envelope’, are predicted to align with the surface provided that they approach with sufficiently steep angle. However simulation of cells swimming against a surface in such a configuration is not possible in the present framework. Simulated human sperm cells performing a planar beat with inclination between the beat plane and the plane-of-flattening of the head were not predicted to glide along surfaces, as has been observed in mouse sperm. Instead, cells initially with the head approximately 1.5–3 μm from the surface were predicted to turn away and escape. The simulation model was also used to examine rolling motility due to elliptical helicoid flagellar beating. The head was found to rotate by approximately 240° over one beat cycle and due to the time-varying torques associated with the flagellar beat was found to exhibit ‘looping’ as has been observed in cells swimming against coverslips

Thermodynamic Aspects of Flagellar Activity

1. The frequencies of the beat of cilia and flagella from various organisms have been determined at temperatures in the range 5-35°C. 2. Values of the activation enthalpy (ΔH{ddagger}, kcal./mole) and activation entropy (ΔS{ddagger}, e.u.) derived from the thermal dependence of frequency show a linear correlation of the form, ΔS{ddagger} = 3.25 ΔH{ddagger}-50.75. 3. The corresponding isokinetic activation free energy is 15.6 kcal./mole. 4. The results support a hypothesis that the breakdown of an ATP-ATPase complex could be the common rate-limiting reaction for flagellar activity. 5. Values of ΔH{ddagger} and ΔS{ddagger} for the decay of length or tension in striated muscles also fall on the same regression line but some smooth muscles show deviations