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.

Thin cylindrical tethers are common lipid bilayer membrane structures, arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the Golgi apparatus. We study the shape and formation of a tether in terms of the classical soap-film problem, which is applied to the case of a membrane disk under tension subject to a point force. A tether forms from the elastic boundary layer near the point of application of the force, for sufficiently large displacement. Analytic results for various aspects of the membrane shape are given.

The motility of organisms is often directed in response to environmental stimuli. Rheotaxis is the directed movement resulting from fluid velocity gradients, long studied in fish, aquatic invertebrates, and spermatozoa. Using carefully controlled microfluidic flows, we show that rheotaxis also occurs in bacteria. Excellent quantitative agreement between experiments with Bacillus subtilis and a mathematical model reveals that bacterial rheotaxis is a purely physical phenomenon, in contrast to fish rheotaxis but in the same way as sperm rheotaxis. This previously unrecognized bacterial taxis results from a subtle interplay between velocity gradients and the helical shape of flagella, which together generate a torque that alters a bacterium's swimming direction. Because this torque is independent of the presence of a nearby surface, bacterial rheotaxis is not limited to the immediate neighborhood of liquid-solid interfaces, but also takes place in the bulk fluid. We predict that rheotaxis occurs in a wide range of bacterial habitats, from the natural environment to the human body, and can interfere with chemotaxis, suggesting that the fitness benefit conferred by bacterial motility may be sharply reduced in some hydrodynamic conditions. low Reynolds number | directional motion | chirality T he effectiveness and benefit of motility are largely determined by the dependence of movement behavior on environmental stimuli. For example, chemical stimuli may affect the spreading of tumor cells (1) and allow bacteria to increase uptake by swimming toward larger nutrient concentrations (2, 3), whereas hydrodynamic stimuli can stifle phytoplankton migration (4), allow protists to evade predators (5), and change sperm-egg encounter rates for external fertilizers (6). Microorganisms exhibit a broad range of directed movement responses, called "taxes". Whereas some of these responses, such as chemotaxis (7) and thermotaxis (8), are active and require the ability to sense and respond to the stimulus, others, such as magnetotaxis (9) and gyrotaxis (4), are passive and do not imply sensing, instead resulting purely from external forces.Chemotaxis is the best studied among these directional motions: Bacteria measure chemical concentrations and migrate along gradients (Fig. 1A). For instance, chemotaxis guides Escherichia coli to epithelial cells in the human gastrointestinal tract, favoring infection (10); Rhizobium bacteria to legume root hairs in soil, favoring nitrogen fixation (2); and marine bacteria to organic matter, favoring remineralization (3). Equally as pervasive as chemical gradients in microbial habitats are gradients in ambient fluid velocity or "shear" (Fig. 1B). Although nearly every fluid environment experiences velocity gradientsfrom laminar shear in bodily conduits and soil to turbulent shear in streams and oceans-the effect of velocity gradients on bacterial motility has received negligible attention compared with chemical gradients, partly due to the difficulty of studying motility under controlled flow conditi...