Cell Invasion Dynamics into a Three Dimensional Extracellular Matrix Fibre Network

The dynamics of filopodia interacting with the surrounding extracellular matrix (ECM) play a key role in various cell-ECM interactions, but their mechanisms of interaction with the ECM in 3D environment remain poorly understood. Based on first principles, here we construct an individual-based, force-based computational model integrating four modules of 1) filopodia penetration dynamics; 2) intracellular mechanics of cellular and nuclear membranes, contractile actin stress fibers, and focal adhesion dynamics; 3) structural mechanics of ECM fiber networks; and 4) reaction-diffusion mass transfers of seven biochemical concentrations in related with chemotaxis, proteolysis, haptotaxis, and degradation in ECM to predict dynamic behaviors of filopodia that penetrate into a 3D ECM fiber network. The tip of each filopodium crawls along ECM fibers, tugs the surrounding fibers, and contracts or retracts depending on the strength of the binding and the ECM stiffness and pore size. This filopodium-ECM interaction is modeled as a stochastic process based on binding kinetics between integrins along the filopodial shaft and the ligands on the surrounding ECM fibers. This filopodia stochastic model is integrated into migratory dynamics of a whole cell in order to predict the cell invasion into 3D ECM in response to chemotaxis, haptotaxis, and durotaxis cues. Predicted average filopodia speed and that of the cell membrane advance agreed with experiments of 3D HUVEC migration at r2 > 0.95 for diverse ECMs with different pore sizes and stiffness.Author Summary: Cell invasion into a 3D ECM requires substantial cellular traction forces as well as the degradation of ECM. We are interested in how filopodia gain traction forces from the surrounding collagen fibers in the degradable ECM. Thereby, to create the overall computational model, we integrated four modules, each capturing a different physical aspect influencing migration: 1) filopodia penetration dynamics; 2) intracellular mechanics; 3) reaction-diffusion mass transfer; and 4) structural mechanics of ECM fiber networks. We successfully compared our model with experiments of 3D HUVEC migration for diverse ECMs with different pore sizes and stiffness. Finally, our model reveals the degradation of ECM fiber network plays an important role in filopodia penetration dynamics during both tugging and contractile phases.