2D data-driven stalk cell prediction model based on tip-stalk cell interaction in angiogenesis

Angiogenesis is the growth process of blood vessels from existing vessels. During angiogenesis, endothelial cells (ECs), which line the vessel, specialize into tip and stalk cells. Tip cells respond to angiogenic signals, burrow into the extracellular matrix (ECM) and form conduits. Stalk cells follow the tip cells along the conduits, and form solid sprouts or lumen vessels. Interactions between stalk cells and tip cells are important for creating functional vessels. The goal of this work is to predict stalk cells migration trajectories from known tip cell trajectories. Four factors influence the position and velocity of cell migration in ECM: cell-cell interaction, drag force, chemotactic signal and cell-ECM interaction. As chemotactic signal and cell-ECM interactions have little effect on stalk cell movement, the proposed model includes the influence of cell-cell interactions and drag force only. The unknown parameters in the model are inferred by Maximum Likelihood Estimation (MLE) from experimental time-lapse cell migration data. Numerical results suggest that the proposed model can accurately predict stalk cell trajectories. The proposed model may be useful for the study of angiogenesis, a critical process for cancer tumor growth.