This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are ``dry'' systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or ``wet'' systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.

Hydrodynamics of soft active matter

The collective migration of cells as a cohesive group is a hallmark of the tissue remodelling events that underlie embryonic morphogenesis, wound repair and cancer invasion. In such migration, cells move as sheets, strands, clusters or ducts rather than individually, and use similar actin- and myosin-mediated protrusions and guidance by extrinsic chemotactic and mechanical cues as used by single migratory cells. However, cadherin-based junctions between cells additionally maintain 'supracellular' properties, such as collective polarization, force generation, decision making and, eventually, complex tissue organization. Comparing different types of collective migration at the molecular and cellular level reveals a common mechanistic theme between developmental and cancer research.

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Collective cell migration in morphogenesis, regeneration and cancer

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.

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Physics of microswimmers--single particle motion and collective behavior: a review.

It has been thought that sheets of cells move by traction forces exerted by the cells at the leading edge of the sheet. Using traction microscopy to create a map of physical forces, it is now shown that in fact it is cells many rows from the front that do most of the work. Fundamental biological processes including morphogenesis, tissue repair and tumour metastasis require collective cell motions1,2,3, and to drive these motions cells exert traction forces on their surroundings4. Current understanding emphasizes that these traction forces arise mainly in ‘leader cells’ at the front edge of the advancing cell sheet5,6,7,8,9. Our data are contrary to that assumption and show for the first time by direct measurement that traction forces driving collective cell migration arise predominately many cell rows behind the leading front edge and extend across enormous distances. Traction fluctuations are anomalous, moreover, exhibiting broad non-Gaussian distributions characterized by exponential tails10,11,12. Taken together, these unexpected findings demonstrate that although the leader cell may have a pivotal role in local cell guidance, physical forces that it generates are but a small part of a global tug-of-war involving cells well back from the leading edge.

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Physical forces during collective cell migration

Metastasis is a complex, multistep process responsible for >90% of cancer-related deaths. In addition to genetic and external environmental factors, the physical interactions of cancer cells with their microenvironment, as well as their modulation by mechanical forces, are key determinants of the metastatic process. We reconstruct the metastatic process and describe the importance of key physical and mechanical processes at each step of the cascade. The emerging insight into these physical interactions may help to solve some long-standing questions in disease progression and may lead to new approaches to developing cancer diagnostics and therapies.

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The physics of cancer: the role of physical interactions and mechanical forces in metastasis

Using an original microfabrication-based technique, we experimentally study situations in which a virgin surface is presented to a confluent epithelium with no damage made to the cells. Although inspired by wound-healing experiments, the situation is markedly different from classical scratch wounding because it focuses on the influence of the free surface and uncouples it from the other possible contributions such as cell damage and/or permeabilization. Dealing with Madin-Darby canine kidney cells on various surfaces, we found that a sudden release of the available surface is sufficient to trigger collective motility. This migration is independent of the proliferation of the cells that mainly takes place on the fraction of the surface initially covered. We find that this motility is characterized by a duality between collective and individual behaviors. On the one hand, the velocity fields within the monolayer are very long range and involve many cells in a coordinated way. On the other hand, we have identified very active "leader cells" that precede a small cohort and destabilize the border by a fingering instability. The sides of the fingers reveal a pluricellular actin "belt" that may be at the origin of a mechanical signaling between the leader and the followers. Experiments performed with autocrine cells constitutively expressing hepatocyte growth factor (HGF) or in the presence of exogenous HGF show a higher average velocity of the border and no leader.

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A. Hertzog

Papers

Collective migration of an epithelial monolayer in response to a model wound