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.

During the formation of tissues, cells organize collectively by cell division and apoptosis. The multicellular dynamics of such systems is influenced by mechanical conditions and can give rise to cell rearrangements and movements. We develop a continuum description of tissue dynamics, which describes the stress distribution and the cell flow field on large scales. In the absence of division and apoptosis, we consider the tissue to behave as an elastic solid. Cell division and apoptosis introduce stress sources that, in general, are anisotropic. By combining cell number balance with dynamic equations for the stress source, we show that the tissue effectively behaves as a viscoelastic fluid with a relaxation time set by the rates of division and apoptosis. If the system is confined in a fixed volume, it reaches a homeostatic state in which division and apoptosis balance. In this state, cells undergo a diffusive random motion driven by the stochasticity of division and apoptosis. We calculate the expression for the effective diffusion coefficient as a function of the tissue parameters and compare our results concerning both diffusion and viscosity to simulations of multicellular systems using dissipative particle dynamics.active fluids | fluctuations | growth processes | source stress M any biological processes, such as organ development or cancerous tumor growth, involve the remodeling of tissues by cell division and cell death or apoptosis. For many years, emphasis has been put on the regulation of growth by signaling pathways such as growth factors and its genetic control (1, 2). Recently, however, the importance of the mechanical properties of tissues has been realized (3-7). It has been shown, for example, that during the development of the fruit fly Drosophila, the expression of some of the essential genes can be strongly modified by the application of external forces that change the local mechanical stresses acting on the cells in the growing organism (8). At certain stages of development, such as gastrulation, the spatial distribution of mechanical stresses also seems to play a role in controlling the pattern of gene expression (9). Quite similarly, in tumor progression, gene expression is related to the stress distribution in the tumor (7,10).The rates of cell division and cell death depend on many biological parameters, but they also depend on the local cell density or pressure in the tumor. It has recently been argued that the tissue pressure at which cell death exactly compensates cell division is an important parameter that could be related to the invasiveness of a tumor in a host tissue (11). Such a pressure has been called homeostatic pressure, and the corresponding tissue steady state, the homeostatic state. This pressure is defined as the isotropic part of the stress acting on cells directly and is not related in any simple way to the hydrostatic pressure.From a mechanical point of view, a tissue is a complex system where the growth due to cell division and cell death interferes with the elastic de...

Although collective cell motion plays an important role, for example during wound healing, embryogenesis, or cancer progression, the fundamental rules governing this motion are still not well understood, in particular at high cell density. We study here the motion of human bronchial epithelial cells within a monolayer, over long times. We observe that, as the monolayer ages, the cells slow down monotonously, while the velocity correlation length first increases as the cells slow down but eventually decreases at the slowest motions. By comparing experiments, analytic model, and detailed particle-based simulations, we shed light on this biological amorphous solidification process, demonstrating that the observed dynamics can be explained as a consequence of the combined maturation and strengthening of cell−cell and cell−substrate adhesions. Surprisingly, the increase of cell surface density due to proliferation is only secondary in this process. This analysis is confirmed with two other cell types. The very general relations between the mean cell velocity and velocity correlation lengths, which apply for aggregates of self-propelled particles, as well as motile cells, can possibly be used to discriminate between various parameter changes in vivo, from noninvasive microscopy data.collective cell migration | jamming | glass transition | dynamic inhomogeneity | cell−cell adhesion C ollective motion of cells is crucial in many biological phenomena, including embryonic development (1), wound healing (2, 3), tissue repair (1, 4), and cancer (1, 4). Therefore, understanding the physics underlying how individually migrating cells combine their motion to collectively migrate is presently a matter of intense study. In this context, several studies have recently shown, by numerical simulations, that local alignment rules can result in the emergence of strongly correlated cellular motions in a confluent monolayer (5-9).As time passes, these cell movements in the monolayer slow down. This classic observation is usually associated with the socalled "density-mediated contact inhibition of locomotion" (10, 11). To go further in the analysis of this phenomenon, several observations (6, 12, 13) and simulations (7,14,15) give an interesting new angle by emphasizing the analogy between a cell monolayer and a bidimensional "jammed" colloidal system, where the individual motions of the particles are confined in "cages" of the size of the particles, and where the whole system behaves as a solid (16)(17)(18)(19). In particular, the increase in the characteristic length scales describing the velocity field as well as the presence of "giant" density fluctuations (20, 21) appear to validate this analogy. As a consequence, several theoretical descriptions have been proposed for these cell assemblies within the conceptual framework used to describe jamming in active systems (6,12,13,(22)(23)(24).Cellular density (the equivalent of the packing fraction in colloidal systems) is often assumed to be the principal control parameter in these system...

Propulsion by cilia is a fascinating and universal mechanism in biological organisms to generate fluid motion on the cellular level. Cilia are hair-like organelles, which are found in many different tissues and many uni-and multicellular organisms. Assembled in large fields, cilia beat neither randomly nor completely synchronously-instead they display a striking self-organization in the form of metachronal waves (MCWs). It was speculated early on that hydrodynamic interactions provide the physical mechanism for the synchronization of cilia motion. Theory and simulations of physical model systems, ranging from arrays of highly simplified actuated particles to a few cilia or cilia chains, support this hypothesis. The main questions are how the individual cilia interact with the flow field generated by their neighbors and synchronize their beats for the metachronal wave to emerge and how the properties of the metachronal wave are determined by the geometrical arrangement of the cilia, like cilia spacing and beat direction. Here, we address these issues by large-scale computer simulations of a mesoscopic model of 2D cilia arrays in a 3D fluid medium. We show that hydrodynamic interactions are indeed sufficient to explain the self-organization of MCWs and study beat patterns, stability, energy expenditure, and transport properties. We find that the MCW can increase propulsion velocity more than 3-fold and efficiency almost 10-fold-compared with cilia all beating in phase. This can be a vital advantage for ciliated organisms and may be interesting to guide biological experiments as well as the design of efficient microfluidic devices and artificial microswimmers.active matter | mesoscale hydrodynamics | dynamical self-organization F luid transport and locomotion due to motile cilia are ubiquitous phenomena in biological organisms on the cellular level (1, 2). Motile cilia are found in many different tissues-from the brain (3) to the lung and the oviduct-and in many uni-and multicellular organisms-from Clamydomonas (4) and Volvox (5, 6) algae to Paramecium. Motile cilia on the surface of a cell perform an active whip-like motion, which propels the fluid along the surface of cells and tissues. In motile cilia, the beat consists of a fast power stroke in which the cilium has an elongated shape and a slower recovery stroke in which the cilium is curved and closer to the cell surface (Fig. 1A). Due to their typical size in the range of 5-20 μm length and 0.25-1.0 μm thickness, the dynamics of cilia in a fluid are dominated by the balance of force generated by motor proteins (7,8) and fluid viscosity and are thus characterized by small-Reynolds-number hydrodynamics (9). Cilia sometimes act together in pairs, such as in the breast-stroke-like motion of Clamydomonas (4), but much more often in large arrays, such as on the surface of Paramecium and Opalina or the tissue lining the airways of the lung. In all these cases, the beat of different cilia is not random, but strongly synchronized. For many cilia arrays, a wave-like pa...

PACS 82.70.-y-Disperse systems; complex fluids PACS 45.50.-j-Dynamics and kinematics of a particle and a system of particles PACS 05.40.-a-Fluctuation phenomena, random processes, noise, and Brownian motion Abstract-The dynamics of a self-propelled Brownian sphere confined between two planar hard walls is investigated by computer simulations and analytic solutions of the corresponding Fokker-Planck equation. It is shown that an accumulation of self-propelled particles, often linked to the hydrodynamic dipole interaction, can be already obtained from the combination of Brownian motion and self-propulsion. The surface excess is calculated as a function of particle velocity, wall separation, and translational and rotational diffusion coefficients. In limits of narrow channels or small propulsion velocities, analytical solutions and numerical results are in excellent agreement.

Recent experiments have shown that spreading epithelial sheets exhibit a long-range coordination of motility forces that leads to a buildup of tension in the tissue, which may enhance cell division and the speed of wound healing. Furthermore, the edges of these epithelial sheets commonly show finger-like protrusions whereas the bulk often displays spontaneous swirls of motile cells. To explain these experimental observations, we propose a simple flocking-type mechanism, in which cells tend to align their motility forces with their velocity. Implementing this idea in a mechanical tissue simulation, the proposed model gives rise to efficient spreading and can explain the experimentally observed long-range alignment of motility forces in highly disordered patterns, as well as the buildup of tensile stress throughout the tissue. Our model also qualitatively reproduces the dependence of swirl size and swirl velocity on cell density reported in experiments and exhibits an undulation instability at the edge of the spreading tissue commonly observed in vivo. Finally, we study the dependence of colony spreading speed on important physical and biological parameters and derive simple scaling relations that show that coordination of motility forces leads to an improvement of the wound healing process for realistic tissue parameters.

The precise role of the microenvironment on tumor growth is poorly understood. Whereas the tumor is in constant competition with the surrounding tissue, little is known about the mechanics of this interaction. Using a novel experimental procedure, we study quantitatively the effect of an applied mechanical stress on the long-term growth of a spheroid cell aggregate. We observe that a stress of 10kPa is sufficient to drastically reduce growth by inhibition of cell proliferation mainly in the core of the spheroid. We compare the results to a simple numerical model developed to describe the role of mechanics in cancer progression.

Sperm are propelled by an actively beating tail, and display a wide variety of swimming patterns. When confined between two parallel walls, sperm swim either in circles or on curvilinear trajectories close to the walls. We employ mesoscale hydrodynamics simulations in combination with a mechanical sperm model to study the swimming behavior near walls. The simulations show that sperm become captured at the wall due to the hydrodynamic flow fields which are generated by the flagellar beat. The circular trajectories are determined by the chiral asymmetry of the sperm shape. For strong (weak) chirality, sperm swim in tight (wide) circles, with the beating plane of the flagellum oriented perpendicular (parallel) to the wall. For comparison, we also perform simulations based on a local anisotropic friction of the flagellum. In this resistive force approximation, surface adhesion and circular swimming patterns are obtained as well. However, the adhesion mechanism is now due to steric repulsion, and the orientation of the beating plane is different. Our model provides a theoretical framework that explains several distinct swimming behaviors of sperm near and far from a wall. Moreover, the model suggests a mechanism by which sperm navigate in a chemical gradient via a change of their shape.