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

Targeting signaling pathways that drive cancer cell migration or proliferation is a common therapeutic approach. A popular experimental technique, the scratch assay, measures the migration and proliferation-driven cell closure of a defect in a confluent cell monolayer. These assays do not measure dynamic effects. To improve analysis of scratch assays, we combine high-throughput scratch assays, video microscopy, and system identification to infer partial differential equation (PDE) models of cell migration and proliferation. We capture the evolution of cell density fields over time using live cell microscopy and automated image processing. We employ weak form-based system identification techniques for cell density dynamics modeled with first-order kinetics of advection-diffusion-reaction systems. We present a comparison of our methods to results obtained using traditional inference approaches on previously analyzed 1-dimensional scratch assay data. We demonstrate the application of this pipeline on high throughput 2-dimensional scratch assays and find that low levels of trametinib inhibit wound closure primarily by decreasing random cell migration by approximately 20%. Our integrated experimental and computational pipeline can be adapted for quantitatively inferring the effect of biological perturbations on cell migration and proliferation in various cell lines.