  Several micro-organisms, such as bacteria, algae, or spermatozoa, use
flagella or cilia 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. 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. 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, $V\sim
A^2/\eta^2$, whereas at large enough A, V is independent of the force and is
determined solely by the stroke frequency and swimmer size. This finding
starkly contrasts with currently known results found from swimming models where
motion is based on flagellar or ciliary activity, where $V\sim A/\eta$. 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.
