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 micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of 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, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slender-body theory to flagellar locomotion. After examining 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. (Some figures in this article are in colour only in the electronic version) This article was invited by Christoph Schmidt.

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The hydrodynamics of swimming microorganisms

Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns. For example, bacterial flagella are helically shaped and driven at their bases by a reversible rotary engine, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.

Microscopic artificial swimmers

1. Introduction to the cell Part I. Rods and Ropes: 2. Polymers 3. Two-dimensional networks 4. Three-dimensional networks Part II. Membranes: 5. Biomembranes 6. Membrane undulations Part III. The Whole Cell: 7. The simplest cells 8. Intermembrane forces 9. Dynamic filaments 10. Mechanical designs Appendix A. Animal cells and tissues Appendix B. The cell's molecular building blocks Appendix C. Elementary statistical mechanics Appendix D. Elasticity References Index.

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Mechanics of the cell

Microrobots have the potential to dramatically change many aspects of medicine by navigating through bodily fluids to perform targeted diagnosis and therapy. Researchers have proposed numerous micro-robotic swimming methods, with the vast majority utilizing magnetic fields to wirelessly power and control the microrobot. In this paper, we compare three promising methods of microrobot swimming (using magnetic fields to rotate helical propellers that mimic bacterial flagella, using magnetic fields to oscillate a magnetic head with a rigidly attached elastic tail, and pulling directly with magnetic field gradients) considering practical hardware limitations in the generation of magnetic fields. We find that helical propellers and elastic tails have very comparable performance, and they generally become more desirable than gradient pulling as size decreases and as distance from the magnetic-field-generation source increases. We provide a discussion of why helical propellers are likely the best overall choice for in vivo applications.

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How Should Microrobots Swim

This is an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random coil. Many studies on semiflexible polymers and their assemblies have been motivated by their importance in biology. Indeed, cross-linked networks of semiflexible polymers form a major structural component of tissue and living cells. Reconstituted networks of such biopolymers have emerged as a new class of biological soft matter systems with remarkable material properties, which have spurred many of the theoretical developments discussed here. Starting from the mechanics and dynamics of individual semiflexible polymers, the physics of semiflexible bundles, entangled solutions, and disordered cross-linked networks are reviewed. Finally, recent developments on marginally stable fibrous networks, which exhibit critical behavior similar to other marginal systems such as jammed soft matter, are discussed.

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Modeling semiflexible polymer networks

http://www.damtp.cam.ac.uk/user/gold/pdfs/trapping.pdf

Trapping and wiggling: elastohydrodynamics of driven microfilaments.

We probed the bending of actin subject to external forcing and viscous drag. Single actin filaments were moved perpendicular to their long axis in an oscillatory way by means of an optically tweezed latex bead attached to one end of the filaments. Shapes of these polymers were observed by epifluorescence microscopy. They were found to be in agreement with predictions of semiflexible polymer theory and slender-body hydrodynamics. A persistence length of 7.460.2 mm could be extracted. @S1063-651X~97!50808-7# PACS number~s!: 87.10.1e, 83.10.Nn, 42.62.2b

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Elastohydrodynamic study of actin filaments using fluorescence microscopy

Acting on actin: The electric motility assay

We present a general theoretical analysis of semiflexible filaments subject to viscous drag or point forcing. These are the relevant forces in dynamic experiments designed to measure biopolymer bending moduli. By analogy with the ``Stokes problems" in hydrodynamics (fluid motion induced by that of a wall bounding a viscous fluid), we consider the motion of a polymer one end of which is moved in an impulsive or oscillatory way. Analytical solutions for the time-dependent shapes of such moving polymers are obtained within an analysis applicable to small-amplitude deformations. In the case of oscillatory driving, particular attention is paid to a characteristic length determined by the frequency of oscillation, the polymer persistence length, and the viscous drag coefficient. Experiments on actin filaments manipulated with optical traps confirm the scaling law predicted by the analysis and provide a new technique for measuring the elastic bending modulus. A re-analysis of several published experiments on microtubules is also presented.

D. Riveline

Papers

Trapping and wiggling: elastohydrodynamics of driven microfilaments.

Elastohydrodynamic study of actin filaments using fluorescence microscopy

Acting on actin: The electric motility assay

Trapping and Wiggling: Elastohydrodynamics of Driven Microfilaments