Quantitative characterization of cell invasion in vitro: formulation and validation of a mathematical model of the collagen gel invasion assay.

An in vitro assay proposed to systematically characterize and compare cell invasion under different conditions is the collagen gel invasion assay where cells, initially seeded onto the surface of a type I collagen gel, penetrate the surface and migrate within the gel over time. Using simplifying assumptions about cell transport across the gel surface and migration within the gel, we formulate and solve a mathematical model of this assay which predicts the resulting cell distribution based on three phenomenological parameters characterizing the ability of cells to penetrate the gel surface interface, migrate randomly within the gel, and return to the gel surface. An index of cell invasiveness is defined based on these parameters that reflects the overall ability of cells to transport across the gel surface interface, that is, invade the gel. Cell concentration profiles predicted by the model correspond well to measured profiles for murine melanoma cells invading gels supplemented with extracellular matrix proteins fibronectin and type IV collagen as well as unsupplemented gels, allowing these parameters to be estimated by a nonlinear regression fit of the model solution to the measured profiles. Our analysis suggests that type IV collagen and fibronectin primarily modulate cell transport across the gel surface interface rather than migration within the gel. Further, we validate the key model assumptions and obtain independent, direct estimates of model parameters by time-lapse video microscopy and digital image analysis of cell penetration of the gel surface and migration within the gel during the assay.