The importance of water-air interfaces (WAI) on microorganism activities has been recognized by many researchers. In this paper, we report a novel phenomenon: the entrapment of ciliates Tetrahymena at the WAI. We first characterized the behavior of cells at the interface and showed that the cells' swimming velocity was considerably reduced at the WAI. To verify the possible causes of the entrapment, we investigated the effects of positive chemotaxis for oxygen, negative geotaxis and surface properties. Even though the taxes were still effective, the entrapment phenomenon was not dependent on the physiological conditions, but was instead affected by the physical properties at the interface. This knowledge is useful for a better understanding of the physiology of microorganisms at interfaces in nature and in industry.
We have studied the collective motion of polar active particles confined to ellipsoidal surfaces. The geometric constraints lead to the formation of vortices that encircle surface points of constant curvature (umbilics). We have found that collective motion patterns are particularly rich on ellipsoids with four umbilics where vortices tend to be located near pairs of umbilical points to minimize their interaction energy. Our results provide a new perspective on the migration of living cells, which most likely use the information provided from the curved substrate geometry to guide their collective motion.Introduction -Active particles are known to spontaneously form complex dynamic patterns at length scales ranging from the molecular [1], to the cellular [2,3] up to macroscopic patterns seen in flocking birds [4], schooling fish [5] or humans in crowded environments [6,7]. The key feature of these active systems is the constant energy input on each individual unit, which renders the system completely out of equilibrium. Collective phenomena in such active systems have been successfully described using so-called self-propelled particle models [8] that are limited to close neighbour interactions only [9]. In unconstrained 2D and 3D systems these models display selforganised pattern formation resembling experimental observations [9]. The behaviour of active particles confined to a surface has been mainly studied on planar surfaces of zero Gaussian curvature. It is known however, that the presence of intrinsic surface curvature frustrates local order giving rise to novel physics [10], as has been shown for 2D fluids confined to curved surfaces [11]. As a consequence of the Poincaré-Hopf theorem, for instance, it is not possible to have continuous fluid flow on the entire surface of a sphere, which requires the presence of two +1 defects (vortices) [12]. The effect of non-zero Gaussian curvature on self-propelled particles remains poorly understood, with only a few recent examples studying the effect of spherical constraints [13,14]. In living systems, cells are influenced by surface curvature as demonstrated by cell movements in the developing corneal epithelium leading to vortex patterns [15] or by the coordinated collective migration of cells during embryonic development [16]. The emergent behaviour of moving cells is not only the result of intercellular interactions, but is crucially influenced by geometrical constraints [2,17,18]. The aim of the current work is to investigate the impact of non-constant Gaussian curvature constraints on the collective behaviour of self-propelled particles. Our restriction of the geometry of the surfaces to ellipsoids allows an analysis of how geometrical cues (represented by the umbilical points of the surface, Fig. 1c) effectively interact with defects in the director-field (e.g., vortices). The strong coupling between vortex position and umbilical points demonstrates the importance of surface geometry on the emergence of patterns in active systems.
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