Run-and-Tumble Dynamics of Self-Propelled Particles in Confinement

Run-and-tumble dynamics is a wide-spread mechanism of swimming bacteria. The accumulation of run-and-tumble microswimmers near impermeable surfaces is studied theoretically and numerically in the low-density limit in two and three spatial dimensions. Both uni-modal and exponential distributions of the run lengths are considered. Constant run lengths lead to {peaks and depletions regions} in the density distribution of particles near the surface, in contrast to {exponentially-distributed run lengths}. Finally, we present a universal accumulation law for large channel widths, which applies not only to run-and-tumble swimmers, but also to many other kinds of self-propelled particles

Giant adsorption of microswimmers: duality of shape asymmetry and wall curvature

The effect of shape asymmetry of microswimmers on their adsorption capacity at confining channel walls is studied by a simple dumbbell model. For a shape polarity of a forward-swimming cone, like the stroke-averaged shape of a sperm, extremely long wall retention times are found, caused by a non-vanishing component of the propulsion force pointing steadily into the wall, which grows exponentially with the self-propulsion velocity and the shape asymmetry. A direct duality relation between shape asymmetry and wall curvature is proposed and verified. Our results are relevant for the design microswimmer with controlled wall-adhesion properties. In addition, we confirm that pressure in active systems is strongly sensitive to the details of the particle-wall interactions.Comment: 6 pages, 7 figure

Sperm and Cilia Dynamics

Spermien schwimmen durch Flüssigkeiten mithilfe einer aktiven schlangenförmigen Bewegung ihres Schwanzes, dem Flagellum. Experimentell hat sich herausgestellt, dass sich Spermien stets an Oberflächen ansammeln. An der Oberfläche schwimmen sie dann in einer kreisförmiger Bewegung, deren Ausrichtung von der Spezies abhängt. Zilien sind haarähnliche Zellfortsätze, die mit einer peitschenförmigen Bewegung Flüssigkeit, oder die Zelle, bewegen. Zilien finden sich in den verschiedensten Organismen. Zum Beispiel benutzt das Pantoffeltierchen Zilien zur Fortbewegung, während in der menschlichen Lunge Zilien Schleim und Fremdkörper heraus transportieren. Das spannendste Phänomen, welches man bei Zilien beobachten kann, ist wohl die "Metachronal Wave". Wenn viele Zilien gemeinsam schlagen, bildet sich spontan ein Wellenmuster aus, ganz ähnlich dem eines Weizenfeldes im Wind. Zilien und Flagellen haben eine gemeinsame Struktur, das Axonem. Wir simulieren ein Modellaxonem aus drei semiflexiblen Polymerstäben die zu einer kranähnlichen Struktur zusammengefasst sind. Mithilfe einer mesoskopischen Simulationsmethode, genannt Multi-Particle Collision Dynamics (MPCD), werden hydrodynamische Wechselwirkungen berücksichtigt. Im Zuge dieser Arbeit wird MPCD zum ersten Mal erfolgreich auf aktive biologische Systeme angewandt. In Simulationen von Spermien wird die Axonemstruktur chiral um einen Kopf ergänzt. Es zeigt sich, dass die Schwimmtrajektorie des Spermiums stark vom Grad der Chiralität abhängt. In freier Flüssigkeit finden wir einen dynamischen Übergang der Trajektorie zwischen einer ausgeprägten Helix und einer fast geradlinigen Bewegung. In der Nähe einer Wand können wir sowohl die Adhäsion an der Grenzfläche, als auch die orientierte kreisförmige Bewegung reproduzieren. Die Ursache für die Adhäsion an der Wand findet sich interessanterweise in der Abstossung des Flagellums von der Wand. Kreisförmige Bewegung und Richtung werden hingegen von der Chiralität des Spermiums bestimmt. Zur Untersuchung der Ziliendynamik wird ein Gitter von typischerweise 20 mal 20 Zilien betrachtet, in dem Axonemstrukturen senkrecht auf einer Wand verankert werden. Das Schlagmuster der Zilien wird der biologischen Situation nachempfunden. Dabei ist entscheidend, dass das Schlagmuster duch äussere Einflüsse modifiziert werden kann, so dass die Entstehung einer Metachronal Wave durch Synchronisation verschiedener Zilien ermöglicht wird. Zum ersten Mal sind wir in der Lage, die Metachronal Wave auf einer ausgedehnten Fläche unabhängig schlagender Zilien in Simulationen zu beobachten. Es zeigt sich, dass die Metachronal Wave gravierende Auswirkungen auf Transportgeschwindigkeit und Effizienz hat. Die durchschnittliche Geschwindigkeit der Flüssigkeit steigt durch die Metachronal Wave um bis zu einem Faktor 3.2 im Vergleich zu einem gleichartigen, synchron schlagenden System. Da gleichzeitig die Leistungsaufnahme sinkt, steigt zudem die Effizienz um bis zu einer Grössenordnung. Weiterhin charakterisieren wir Transport und Welleneigenschaften als Funktionen der Schlagrichtung, dem Zilienabstand und der Viskosität der Flüssigkeit. Wir sind überzeugt, dass sowohl die Effizienz als auch im besonderen die Transportgeschwindigkeit entscheidend sind für die Fitness der Zelle. Die Metachronal wave ist daher von grosser funktionaler Bedeutung für Zellen mit Zilien

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

Self-propelled Worm-like Filaments: Spontaneous Spiral Formation, Structure, and Dynamics

Worm-like filaments that are propelled homogeneously along their tangent vector are studied by Brownian dynamics simulations. Systems in two dimensions are investigated, corresponding to filaments adsorbed to interfaces or surfaces. A large parameter space covering weak and strong propulsion, as well as flexible and stiff filaments is explored. For strongly propelled and flexible filaments, the free-swimming filaments spontaneously form stable spirals. The propulsion force has a strong impact on dynamic properties, such as the rotational and translational mean square displacement and the rate of conformational sampling. In particular, when the active self-propulsion dominates thermal diffusion, but is too weak for spiral formation, the rotational diffusion coefficient has an activity-induced contribution given by $v_c/\xi_P$, where $v_c$ is the contour velocity and $\xi_P$ the persistence length. In contrast, structural properties are hardly affected by the activity of the system, as long as no spirals form. The model mimics common features of biological systems, such as microtubules and actin filaments on motility assays or slender bacteria, and artificially designed microswimmers

Self-Propelled Rods near Surfaces

We study the behavior of self-propelled nano- and micro-rods in three dimensions, confined between two parallel walls, by simulations and scaling arguments. Our simulations include thermal fluctuations and hydrodynamic interactions, which are both relevant for the dynamical behavior at nano- to micrometer length scales. In order to investigate the importance hydrodynamic interactions, we also perform Brownian-dynamics-like simulations. In both cases, we find that self-propelled rods display a strong surface excess in confined geometries. An analogy with semi-flexible polymers is employed to derive scaling laws for the dependence on the wall distance, the rod length, and the propulsive force. The simulation data confirm the scaling predictions.Comment: 6 pages, 9 figure

Multi-Ciliated Microswimmers -- Metachronal Coordination and Helical Swimming

The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number N (with 5 < N < 60) of cilia with length comparable to the body radius, is investigated by mesoscale hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e. the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity vswim is found to increase with the cilia number N with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.Comment: 15 pages, 14 figure

A minimal model for structure, dynamics, and tension of monolayered cell colonies

The motion of cells in tissues is an ubiquitous phenomenon. In particular, in monolayered cell colonies in vitro, pronounced collective behavior with swirl-like motion has been observed deep within a cell colony, while at the same time, the colony remains cohesive, with not a single cell escaping at the edge. Thus, the colony displays liquid-like properties inside, in coexistence with a cell-free "vacuum" outside. How can adhesion be strong enough to keep cells together, while at the same time not jam the system in a glassy state? What kind of minimal model can describe such a behavior? Which other signatures of activity arise from the internal fluidity? We propose a novel active Brownian particle model with attraction, in which the interaction potential has a broad minimum to give particles enough wiggling space to be collectively in the fluid state. We demonstrate that for moderate propulsion, this model can generate the fluid-vacuum coexistence described above. In addition, the combination of the fluid nature of the colony with cohesion leads to preferred orientation of the cell polarity, pointing outward, at the edge, which in turn gives rise to a tensile stress in the colony -- as observed experimentally for epithelial sheets. For stronger propulsion, collective detachment of cell clusters is predicted. Further addition of an alignment preference of cell polarity and velocity direction results in enhanced coordinated, swirl-like motion, increased tensile stress and cell-cluster detachment

Cooperation of Sperm in Two Dimensions: Synchronization, Attraction and Aggregation through Hydrodynamic Interactions

Sperm swimming at low Reynolds number have strong hydrodynamic interactions when their concentration is high in vivo or near substrates in vitro. The beating tails not only propel the sperm through a fluid, but also create flow fields through which sperm interact with each other. We study the hydrodynamic interaction and cooperation of sperm embedded in a two-dimensional fluid by using a particle-based mesoscopic simulation method, multi-particle collision dynamics (MPC). We analyze the sperm behavior by investigating the relationship between the beating-phase difference and the relative sperm position, as well as the energy consumption. Two effects of hydrodynamic interaction are found, synchronization and attraction. With these hydrodynamic effects, a multi-sperm system shows swarm behavior with a power-law dependence of the average cluster size on the width of the distribution of beating frequencies