  A phase field approach is proposed to model the chemotaxis of Dictyostelium
discoideum. In this framework, motion is controlled by active forces as
determined by the Meinhardt model of chemical dynamics which is used to
simulate directional sensing during chemotaxis. Then, the movement of the cell
is achieved by the phase field dynamics, while the reaction-diffusion equations
of the Meinhardt model are solved on an evolving cell boundary. This task
requires the extension of the usual phase-field formulation to allow for
components that are restricted to the membrane. The coupled system is
numerically solved by an efficient spectral method under periodic boundary
conditions. Numerical experiments show that our model system can successfully
mimic the typically observed pseudopodia patterns during chemotaxis.
