Simulation of a Free Boundary Cell Migration Model through Physics Informed Neural Networks

Understanding the complexities of single-cell migration is facilitated by computational modeling, which provides important insights into the physiological processes that underlie migration mechanisms. This study developed a computational model for one-dimensional actomyosin flow in a migrating cell with moving boundaries. The model incorporates the complex interplay of actin polymerization, substrate adhesion, and actomyosin dynamics through a system of coupled nonlinear partial differential equations. A physics-informed neural network is designed to understand the dynamic behavior of actin flow and actin concentration within the cell along with the unknown moving boundaries, taking into account the computational cost of solving a dynamic model with a deformable domain. The model's capacity to depict the complex interaction between biological and physical processes within the cell is demonstrated by the numerical results, which qualitatively agree with experimental and computational data available in the literature. This study demonstrates the application of a deep learning method to simulate a challenging biophysical problem with moving boundaries. The model does not require synthetic data for training and accurately reflects the intricate biophysics of cell migration.