  Cells and microorganisms adopt various strategies to migrate in response to
different environmental stimuli. To date, many modeling research has focused on
the crawling-based Dictyostelium discoideum (Dd) cells migration induced by
chemotaxis, yet recent experimental results reveal that even without adhesion
or contact to a substrate, Dd cells can still swim to follow chemoattractant
signals. In this paper, we develop a modeling framework to investigate the
chemotaxis induced amoeboid cell swimming dynamics. A minimal swimming system
consists of one deformable Dd amoeboid cell and a dilute suspension of
bacteria, and the bacteria produce chemoattractant signals that attract the Dd
cell. We use the mathematical amoeba model to generate Dd cell deformation and
solve the resulting low Reynolds number flows, and use a moving mesh based
finite volume method to solve the reaction-diffusion-convection equation. Using
the computational model, we show that chemotaxis guides a swimming Dd cell to
follow and catch bacteria, while on the other hand, bacterial rheotaxis may
help the bacteria to escape from the predator Dd cell.
