Stochastic and Heterogeneous Cancer Cell Migration: Experiment and Theory*

Cell migration is an essential process in the cancer metastasis. A mathematical model for the cell migration would help understand cancer metastasis and might propose a new approach for cancer treatment. Models based on the diffusion equation have been developed because the cell migration looks similar to a random walk. However, recent studies showed that cell migration should be non-Fickian and undergo non-Gaussian diffusion, thus implying that a new model beyond the diffusion equation would be necessary. Here, we propose a mathematical model for anomalous cell migration by introducing two types of heterogeneity in the cell population: cellular heterogeneity and temporal heterogeneity. We investigate 2D migration of A549 cells and find that the migration of A549 cells is non-Gaussian but Fickian diffusion. We employ four different models to elucidate anomalous cell migration: homogeneous (HO), cellular heterogeneity (CH), temporal heterogeneity (TH) and cellular-temporal heterogeneity (CTH) model. We show that only CTH model can describe anomalous cell migration and that considering both cellular and temporal heterogeneity together is crucial to understanding the cell migration.