The impact of oxygen heterogeneity on epithelial-mesenchymal transitions: a numerical study.

The epithelial-mesenchymal transition (EMT), a key stage in tumor metastasis and invasion, depends on many micro-environmental factors, including oxygen levels. In this article, we use a continuum partial differential equations (PDEs) framework comprising coupled equations for the epithelial, mesenchymal, and necrotic cell densities and oxygen concentration to unravel the mysteries of how oxygen heterogeneity affects EMT. A distinguishing feature of the model is that the rates of EMT and MET (mesenchymal-epithelial transition) depend on the oxygen concentration. We assume EMT occurs when oxygen concentration drops below a critical level, and MET occurs when it rises above the critical value. We begin by studying EMT dynamics in an in vitro scenario, where oxygen levels are assumed to be spatially uniform and fluctuate over time between normoxia and hypoxia. This setup mimics aspects of the in vivo phenomenon of cyclic hypoxia. Numerical simulations indicate that the tumor cells adopt a single phenotype based on the oxygen levels: under normoxic conditions, the cells exhibit an epithelial phenotype, while under hypoxic conditions, they transition to a mesenchymal phenotype. We also observe that temporal changes in oxygen levels affect the tumor's overall growth rate. Specifically, our investigations reveal that as the timescale of the oxygen fluctuations decreases, the tumor's growth rate increases. We then use the model to study an in vivo scenario in which we account for oxygen diffusion in order to investigate the effect of spatial heterogeneity in oxygen levels on the EMT dynamics. Simulation results indicate that spatial oxygen heterogeneity generates a heterogeneous population within the tumor, with epithelial cells localized on the outer rim of the tumor and mesenchymal cells concentrated at the tumor center. We perform additional simulations which show further that an increase in mesenchymal diffusivity increases the density of the epithelial cells and the tumor's volume.