The self-propelled microswimmers have recently attracted considerable attention as model systems for biological cell migration as well as artificial micromachines. A simple and well-studied microswimmer model consists of three identical spherical beads joined by two springs in a linear fashion with active oscillatory forces being applied on the beads to generate self-propulsion. We have extended this linear microswimmer configuration to a triangular geometry where the three beads are connected by three identical springs in an equilateral triangular manner. The active forces acting on each spring can lead to autonomous steering motion; i.e., allowing the swimmer to move along arbitrary paths. We explore the microswimmer dynamics analytically and pinpoint its rich character depending on the nature of the active forces. The microswimmers can translate along a straight trajectory, rotate at a fixed location, as well as perform a simultaneous translation and rotation resulting in complex curved trajectories. The sinusoidal active forces on the three springs of the microswimmer contain naturally four operating parameters which are more than required for the steering motion. We identify the minimal operating parameters which are essential for the motion of the microswimmer along any given arbitrary trajectory. Therefore, along with providing insights into the mechanics of the complex motion of the natural and artificial microswimmers, the triangular three-bead microswimmer can be utilized as a model for targeted drug delivery systems and autonomous underwater vehicles where intricate trajectories are involved.

Mammalian cells developed two main migration modes. The slow mesenchymatous mode, like crawling of fibroblasts, relies on maturation of adhesion complexes and actin fibre traction, while the fast amoeboid mode, observed exclusively for leukocytes and cancer cells, is characterized by weak adhesion, highly dynamic cell shapes, and ubiquitous motility on 2D and in 3D solid matrix. In both cases, interactions with the substrate by adhesion or friction are widely accepted as a prerequisite for mammalian cell motility, which precludes swimming. We show here experimental and computational evidence that leukocytes do swim, and that efficient propulsion is not fuelled by waves of cell deformation but by a rearward and inhomogeneous treadmilling of the cell external membrane. Our model consists of a molecular paddling by transmembrane proteins linked to and advected by the actin cortex, whereas freely diffusing transmembrane proteins hinder swimming. Furthermore, continuous paddling is enabled by a combination of external treadmilling and selective recycling by internal vesicular transport of cortex-bound transmembrane proteins. This mechanism explains observations that swimming is five times slower than the retrograde flow of cortex, and also that lymphocytes are motile in non-adherent confined environments. Resultantly, the ubiquitous ability of mammalian amoeboid cells to migrate in 2D or 3D, and with or without adhesion, can be explained for lymphocytes by a single machinery of heterogeneous membrane treadmilling. SIGNIFICANCE STATEMENT Leukocytes have a ubiquitous capacity to migrate on or in solid matrices, and with or without adhesion, which is instrumental to fight infections. The precise mechanisms sustaining migration remain however arguable. It is for instance widely accepted that leukocytes cannot crawl on 2D substrates without adhesion. In contrast, we showed that human lymphocytes swim on nonadherent 2D substrates and in suspension. Furthermore, our experiments and modelling suggest that propulsion rely hardly on cell body deformations and predominantly on molecular paddling by transmembrane proteins protruding outside the cell. For physics, this study reveals a new type of micro-swimmer, and for biology it suggests that leukocytes ubiquitous crawling may have evolved from an early machinery of swimming shared by various eukaryotic cells.