Qualitative study of cell migration associated with hypoxia in the dynamics of tumor growth

Recent results point to the importance of hypoxia in the development of cancer. In particular, hypoxia is generated by an intratumoral oxygen gradient, driving tumor cells towards a migratory phenotype, which in turn promotes invasion and metastatic risk. Recently, experimentalists developed a novel bioengineered reporter system where normoxic cells fluoresce red (DsRed) until exposure to hypoxic conditions, at which point increases in hypoxia-inducible factors (HIFs) induce a permanent genetic change to express green fluorescent protein (GFP). Observations of this system in a mouse model allow us to formulate and evaluate new hypotheses on the frequency and duration of phenotypic changes in cancer cells under the influence of hypoxic conditions. In this work, we present a qualitative study of the response of the GFP+ cells to the migratory stimulus from hypoxia, with a focus on understanding the role of phenotypic transience or permanence on cancer invasion. We use a hybrid continuum-discrete model on two scales that describes the behavior of normoxic and hypoxic cells in the dynamics of tumor growth and invasion. On the cellular scale, the cells are individually represented as discrete agents according to their physical and phenotypic attributions, while on the tissue scale, the dispersion of the oxygen pressure in the microenvironment is represented using continuum diffusion-reaction equations. As in the in vivo experiments, we model changes in red/green fluorescence based on hypoxic exposure. We calibrate changes in cell motility following hypoxic exposure to ex vivo measurements of DsRed+ and GFP+ in cells, using an Approximate Bayesian Computation (ABC) method. The initial results of the in silico model present a plausible representation of the biological experiments and suggest new research themes.