Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection the marine life ecosystem. Here we review biophysical mechanical principles of locomotion at small scales relevant to cell swimming, tens micrometers below. At this scale, inertia unimportant Reynolds number small. Our emphasis on simple physical picture fundamental flow physics phenomena regime. We first give a brief overview mechanisms for swimming motility, basic...

The motility of organisms is often directed in response to environmental stimuli. Rheotaxis the movement resulting from fluid velocity gradients, long studied fish, aquatic invertebrates, and spermatozoa. Using carefully controlled microfluidic flows, we show that rheotaxis also occurs bacteria. Excellent quantitative agreement between experiments with Bacillus subtilis a mathematical model reveals bacterial purely physical phenomenon, contrast fish but same way as sperm rheotaxis. This...

We precisely measure the force-free swimming speed of a rotating helix in viscous and viscoelastic fluids. The fluids are highly to replicate low Reynolds number environment microorganisms. helix, macroscopic scale model for bacterial flagellar filament, is rigid rotated at constant rate while simultaneously translated along its axis. By adjusting translation make net hydrodynamic force vanish, we as function rotation rate, geometry, fluid properties. compare our measurements high-molecular...

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation equations for curves surfaces viscous fluid. The focus is on geometrical aspects simple variational methods calculating internal stresses forces, full nonlinear are derived. In case membranes, particular attention paid to hydrodynamics curved, deforming surface. formalism illustrated two studies: (1) twirling instability straight elastic rod rotating fluid (2) pearling buckling instabilities...

Evolution from unicellular organisms to larger multicellular ones requires matching their needs the rate of exchange molecular nutrients with environment. This logistic problem poses a severe constraint on development. For whose body plan is spherical shell, such as volvocine green algae, current (molecules per second) needed grows quadratically radius, whereas at which diffusion alone exchanges molecules linearly, leading bottleneck radius beyond diffusive cannot meet metabolic demands. By...

The motion of a rotating helical body in viscoelastic fluid is considered. In the case force-free swimming, introduction viscoelasticity can either enhance or retard swimming speed and locomotive efficiency, depending on geometry, properties, rotation rate. Numerical solutions Oldroyd-B equations show how previous theoretical predictions break down with increasing radius decreasing filament thickness. Helices large pitch angle an increase to local maximum at Deborah number order unity....

Many micro-organisms swim through gels and non-Newtonian fluids in their natural environments. In this paper, we focus on which use flagella for propulsion. We address how swimming velocities are affected nonlinearly viscoelastic by examining the problem of an infinitely long cylinder with arbitrary beating motion Oldroyd-B fluid. solve velocity limit deflections from its straight configuration small relative to radius wavelength deflections; furthermore, is compared deflections. find that...

Motivated by our desire to understand the biophysical mechanisms underlying swimming of sperm in non-Newtonian fluids female mammalian reproductive tract, we examine filaments nonlinear viscoelastic upper convected Maxwell model. We obtain velocity and hydrodynamic force exerted on an infinitely long cylinder with prescribed beating pattern. use these results a simplified sliding-filament model for flagellum. Viscoelasticity tends decrease speed, changes patterns due viscoelasticity can...

Abstract Many motile bacteria display wiggling trajectories, which correspond to helical swimming paths. Wiggling trajectories result from flagella pushing off-axis relative the cell body and making wobble. The spatial extent of is controlled by velocity flagellar torque, leads rotation body. We employ method regularized stokeslets investigate produced bundles, can form at many locations orientations for peritrichously flagellated bacteria. Modelling bundle as a rigid helix with fixed...

Watching defects flow and grow Orientational topological in liquid crystals, known as disclinations, have been visualized polymeric materials or through mesoscale simulations of the local orientation molecules. Duclos et al. report experimental visualization structure dynamics disclination loops active, three-dimensional nematics using light-sheet microscopy to watch motion nematic molecules driven by microtubule bundles (see Perspective Bartolo). This setup makes it possible directly...

Escherichia coli and other bacteria use rotating helical filaments to swim. Each cell typically has about four filaments, which bundle or disperse depending on the sense of motor rotation. To study bundling process, we built a macroscopic scale model consisting stepper motor-driven polymer helices in tank filled with high-viscosity silicone oil. The Reynolds number, ratio viscous elastic stresses, helix geometry our experimental approximately match corresponding quantities full-scale E....

Escherichia coli bacteria use rotating helical flagella to swim. At this scale, viscous effects dominate inertia, and there are significant hydrodynamic interactions between nearby helices. These cause the bundle during ``runs'' of bacterial chemotaxis. Here we slender-body theory solve for flow fields generated by rigid helices rotated stationary motors. We determine how forces torques depend on phase difference, show that driven at constant torque do not synchronize, flows. also symmetry...

We show that plane parabolic flow in a microfluidic channel causes nonmotile helically-shaped bacteria to drift perpendicular the shear plane. Net results from preferential alignment of helices with streamlines, direction depends on chirality helix and sign rate. The is good agreement model based resistive force theory, separation efficient (>80%) fast (<2s). estimate effect Brownian rotational diffusion chiral how this method can be extended separate molecules.

Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and fluid solvent. We analyze the swimming of an infinite sheet undergoing transverse traveling wave deformations in "two-fluid" model gel, which treats network solvent two coupled viscous continuum phases. show that geometric nonlinearities must be incorporated to obtain physically...

Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a fluid has on motion beating patterns of elastic filaments. We treat both passive filament which is actuated at one end an active with bending forces arising from internal motors distributed along its length. describe how viscoelasticity modifies hydrodynamic exerted filaments, these modified affect patterns....

Motivated by the observed coordination of nearby beating cilia, we use a scale model experiment to show that hydrodynamic interactions can cause synchronization between rotating paddles driven at constant torque in very viscous fluid. Synchronization is only when shafts supporting have some flexibility. The phase difference synchronized state depends on symmetry paddles. We method regularized stokeslets and find excellent agreement with experimental observations. also simple analytic theory...

We resolve the 3D trajectory and orientation of individual cells for extended times, using a digital tracking technique combined with reconstructions. have used this to study motility uniflagellated bacterium Caulobacter crescentus found that each cell displays two distinct modes motility, depending on sense rotation flagellar motor. In forward mode, when flagellum pushes cell, body is tilted respect direction motion, it precesses, tracing out helical trajectory. reverse pulls precession...

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist bend elasticity. Competition between injection, diffusion, writhing instabilities is described novel pair coupled PDEs for evolution. Analytical numerical methods elucidate twist/bend coupling reveal two dynamical regimes separated Hopf bifurcation: (i) diffusion-dominated axial...

We give a simple theory for recent experiments of Bar-Ziv and Moses [Phys. Rev. Lett. 73, 1392 (1994)] in which tubular vesicles are excited using laser tweezers to ``peristaltic'' state. Considering the hydrodynamics bilayer membrane under tension, we reproduce some qualitative behavior seen find value wavelength instability terms independently measured material parameters, rough agreement with experimental values.

Exploiting the ``natural'' frame of space curves, we formulate an intrinsic dynamics a twisted elastic filament in viscous fluid. Coupled nonlinear equations describing temporal evolution filament's complex curvature and twist density capture dynamic interplay writhe. These are used to illustrate remarkable phenomenon: geometric untwisting open filaments, whereby twisting strains relax through transient writhing instability without axial rotation. Experimentally observed motions fibers...

We measure the swimming speed of a cylindrical version Taylor's sheet in viscoelastic fluids, and find that depending on rheology, can either increase or decrease relative to Newtonian viscous fluid. The stroke is prescribed propagating wave travels along azimuthal direction. measurements are performed with immersed fluid inside tank under torque-free conditions. Swimming speeds case found be consistent calculations using Stokes equation. A faster has viscosity independent shear rate. By...

In bacterial chemotaxis, E. coli cells drift up chemical gradients by a series of runs and tumbles. Runs are periods directed swimming, tumbles abrupt changes in swimming direction. Near the beginning each run, rotating helical flagellar filaments that propel cell form bundle. Using resistive-force theory, we show counterrotation body necessary for torque balance is sufficient to wrap into bundle, even absence swirling flows produced individual filament.