Amoeboid swimming in a channel

Abstract

Several micro-organisms, such as bacteria, algae, or spermatozoa, use flagellar or ciliary activity to swim in a fluid, while many other micro-organisms instead use ample shape deformation, described as amoeboid, to propel themselves by either crawling on a substrate or swimming. Many eukaryotic cells were believed to require an underlying substratum to migrate (crawl) by using membrane deformation (like blebbing or generation of lamellipodia) but there is now increasing evidence that a large variety of cells (including those of the immune system) can migrate without the assistance of focal adhesion, allowing them to swim as efficiently as they can crawl. This paper details the analysis of amoeboid swimming in a confined fluid by modeling the swimmer as an inextensible membrane deploying local active forces (with zero total force and torque). The swimmer displays a rich behavior: it may settle into a straight trajectory in the channel or navigate from one wall to the other depending on its confinement. The nature of the swimmer is also found to be affected by confinement: the swimmer can behave, on the average over one swimming cycle, as a pusher at low confinement, and becomes a puller at higher confinement, or vice versa. The swimmer's nature is thus not an intrinsic property. The scaling of the swimmer velocity V with the force amplitude A is analyzed in detail showing that at small enough A, V ∼ A 2 /η 2 (where η is the viscosity of the ambient fluid), whereas at large enough A, V is independent of the force and is determined solely by the stroke cycle frequency and swimmer size. This finding starkly contrasts with currently known results found from swimming models where motion is based on ciliary and flagellar activity, where V ∼ A/η. To conclude, two definitions of efficiency as put forward in the literature are analyzed with distinct outcomes. We find that one type of efficiency has an optimum as a function of confinement while the other does not. Future perspectives are outlined.

Flow characteristics of Chlamydomonas result in purely hydrodynamic scattering

“…The results further confirm similarity of the behavior for swimmers with different propeller speeds. A similar effect has been also reported for amoeboid swimmers [12,13], where swimming stroke frequency does not change the navigation behavior.…”

“…Few recent theoretical and numerical studies [12,13,14] have shown that specific puller-type swimmers (e.g. deformable swimmers with amoeboid motion) can undergo purely hydrodynamic scattering in a channel (termed as 'navigation swimming' [12]).…”

Eukaryotic cell dynamics from crawlers to swimmers

“…Whether the gradient contributes to or opposes motion under different combinations of contact with a surface can be studied with a computational model that integrates the cortical flow and the re-circulating flow described above. 69,186,187 Computational results from a model using a free-energy-based description of the membrane shows that cells can swim under various combinations of tension gradient in the membrane and heterogeneity of the bending rigidity. 69 Moreover, the direction of migration depends on the balance between the cortical tension gradient and the variation of the bending rigidity.…”

Effect of Cytoskeleton Elasticity on Amoeboid Swimming

“…To see this figure in color, go online. Z f act ðr; tÞdA ¼ 0 (11) and Z rðtÞ Â f act ðr; tÞdA ¼ 0 (12) because the passive forces defined above satisfy automatically the zero force and torque conditions (46). Furthermore, the active forces must be chosen in such a way that the full cycle of shape configurations breaks the time symmetry, as required by the Purcell theorem 47, to lead to a net displacement of the swimmer after a full stroke cycle.…”