Computational and Modeling Strategies for Cell Motility - Computational Modeling of Biological Systems - page 285

In the following, we apply the multiphase complex fluid cell model to an active
cortical layer near the membrane. Everything outside the layer is treated as a viscous
fluid for simplicity. Our goal is to investigate how this cytoskeletal-membrane
coupled model responds to an imposed ATP-activated stress in the cortical layer.

5 Numerical Results and Discussion

The coupled flow and structure equations are solved using a spectral method in 2D
built from analogous multiphase phase field codes [ 94 , 115 , 117 ]. The computed
domain size is Œ0;1 Œ0;1, which we emphasize encompasses the cell and
ambient viscous fluid. The number of grid points in each direction for the reported
simulations is 256. The parameters used are k a D 0:01;K D 0:01;M 1 D 0:1;
M 2 D 1;k B Tk b D 1e 9; 1 D 1; 2 D 0:001;a D 0:8;N D 6; D 0:2; 0 D 4;
1 D 1; s D 1;W 0 D 0:01; D 0:02.

5.1 Activation of a Local Domain in the Cortical Layer

In this simulation, we impose the active region on the left side of the cell within the
cortical layer. The initial shape of the cell and active region are shown in Fig. 1 .As
time evolves, the activated region induces a protrusion in the membrane and cortical

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Fig. 1 Initial shape and
activation domain are
indicated by the contours

0 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9