Generation of a Virtual Cell using a Phase Field Approach to Model Amoeboid Crawling

The process of chemotaxis of living cells is complex. Cells follow gradients of an external signal because the interior of the cells gets polarized. The description of the exterior and the interior of the cell together with its motion for the convenient realization of the computational modeling of the whole process is a complex technical problem. Here, we employ a phase field model to characterize the interior of the cell, permitting the integration of stochastic partial differential equations, responsible for the polarization in the interior of the cell, and simultaneously, the calculation of the shape deformations of the cell, including its locomotion. We detail the mathematical description of the process and the procedure to calculate numerically the phase field with a simple reaction-diffusion equation for a single concentration.