Inference of weak-form partial differential equations describing migration and proliferation mechanisms in wound healing experiments on cancer cells

Cancer metastasis, which requires migration of cancer cells away from the primary tumor, is responsible for approximately 65% percent of cancer-related deaths. Therefore, targeting signaling pathways that drive cancer cell migration or proliferation is a common therapeutic approach. Cell migration is commonly studied using experimental approaches which track cells or cell monolayers as they evolve over time. Computational modeling can then be used to fit partial differential equation (PDE) models to the data, providing mechanistic insights underlying the observed cell motion, including the contribution of various cellular behaviors such as random motion, directed motion, and cell division. A popular experimental technique, the scratch assay, measures the migration and proliferation-driven cell closure of a scratch in a confluent cell monolayer. However, these assays do not disambiguate between different drivers of scratch closure (for instance between cell proliferation and migration to open space). To improve analysis of this technique, we combine scratch assays, video microscopy, and PDE inference to gain quantitative insight to mechanisms of cell migration and proliferation. We capture the evolution of cell density fields over time using live-cell microscopy and automated image processing. Our PDE inference methods involve the use of weak form-based system identification techniques for cell density dynamics modeled with advection-diffusion-reaction systems. We then compare our method with recent modeling work, finding that our model discovery tool automatically identifies similar models including reaction and diffusion terms from a larger set of bases. We demonstrate the application of this framework on 2-dimensional scratch assays subject to the inhibiting effect of trametinib on wound closure and characterize the results in the context of the quantified uncertainty in our inference approach. Our integrated experimental and computational pipeline can be used to rapidly identify and refine models of cell migration in a variety of contexts, enabling the quantitative measurement of the effect of drugs and other perturbations on cell migration and proliferation with uncertainty accounted for.Author summary: Collective cell migration underlies a wide range of biological phenomena, from cancer migration to tissue regeneration. Mathematical models, based on random and directed cell motion and cell birth or death, have been used to understand cell migration in a variety of contexts. However, such models can be time consuming to develop. Here, we advance a model discovery tool which rapidly and automatically identifies parsimonious models of cell migration. We validate our tool against previously analyzed data, and then deploy it to model cell migration in the presence or absence of a chemotherapeutic drug. We find that the drug reduces random cell migration by approximately 40%. We envision our tool being used to rapidly identify quantitative models of cell migration to compare the effects of new drugs or genetic perturbations.