Chemotaxis of a eukaryotic cell in complex gradients of chemoattractants

We studied the chemotaxis of a eukaryotic cell by constructing a mathematical model that takes into account chemical kinetics as well as the cellular shape. A cell is defined as a single domain on discrete two-dimensional grids. In the cellular domain each grid contains three kinds of molecule, an activator and inhibitor of the actin polymerization, and polymerized actins. The external signal promotes production of both activator and inhibitor and thus changes the amount of polymerized actins. If the amount of polymerized actins in a grid of the cell border (i.e., the cellular membrane) is larger than a certain threshold, then a new grid adjacent to the border is assigned to the cellular grid. Upon this change of the cellular shape, constraints are imposed to preserve the cellular volume and to make the length of the cellular border as small as possible. The cell moves in the grid space driven by this change of the cellular shape. We succeeded in reproducing chemotaxis in a linear gradient. For two more complex gradients, the behavior of our cell is consistent with experimental results.This work was presented, in part, at the 9th International Symposium on Artificial Life and Robotics, Oita, Japan, January 28–30, 2004