Epithelial-mesenchymal transition (EMT), the conversion between rigid epithelial cells and motile mesenchymal cells, is a reversible cellular process involved in tumorigenesis, metastasis, and chemoresistance. Numerous studies have found that several types of tumor cells show a high degree of cell-to-cell heterogeneity in terms of their gene expression signatures and cellular phenotypes related to EMT. Recently, the prevalence and importance of partial or intermediate EMT states have been reported. It is unclear, however, whether there is a general pattern of cancer cell distribution in terms of the overall expression of epithelial-related genes and mesenchymal-related genes, and how this distribution is related to EMT process in normal cells. In this study, we performed integrative transcriptomic analysis that combines cancer cell transcriptomes, time course data of EMT in non-tumorigenic epithelial cells, and epithelial cells with perturbations of key EMT factors. Our statistical analysis shows that cancer cells are widely distributed in the EMT spectrum, and the majority of these cells can be described by an EMT path that connects the epithelial and the mesenchymal states via a hybrid expression region in which both epithelial genes and mesenchymal genes are highly expressed overall. We found that key patterns of this EMT path are observed in EMT progression in non-tumorigenic cells and that transcription factor ZEB1 plays a key role in defining this EMT path via diverse gene regulatory circuits connecting to epithelial genes. We performed Gene Set Variation Analysis to show that the cancer cells at hybrid EMT states also possess hybrid cellular phenotypes with both high migratory and high proliferative potentials. Our results reveal critical patterns of cancer cells in the EMT spectrum and their relationship to the EMT process in normal cells, and provide insights into the mechanistic basis of cancer cell heterogeneity and plasticity.

To prevent indefinite cellular responses to external signals, cells utilize various adaptation mechanisms. The yeast mating-response pathway is a model cellular system that exhibits adaptation to persistent external signals. This pathway employs a mitogen-activated protein kinase (MAPK) cascade which is composed of two well-known negative feedback inhibitions that involve the yeast phosphatase proteins Ptp3 and Msg5. The phosphorylated form of the yeast MAPK protein Fus3 (pFus3) triggers the phosphorylation of both phosphatases, but transcriptionally upregulates only Msg5. To study the biological rationale for the existence of two distinct negative feedback inhibitions acting on pFus3, we used published experimental data to develop a mathematical model which quantifies the inhibitory roles of these phosphatase proteins on pFus3. Our analyses show that the inhibition of pFus3 due to Ptp3 is largely independent of the signal profile, and is most impactful at early time points after pheromone induction. Conversely, the feedback inhibition due to Msg5 is highly dependent on the signal profile, and is most influential after pFus3 attains its maximum cellular abundance. Similarly, Ptp3 reduces the variation in the pFus3 dynamics at early time points while the noise-reduction effects of Msg5 become stronger as time passes.