The Mathematics of Phenotypic State Transition: Paths and Potential

2020 ◽  
Vol 100 (3) ◽  
pp. 451-464
Author(s):  
Vimalathithan Devaraj ◽  
Biplab Bose
2019 ◽  
Vol 8 (7) ◽  
pp. 911 ◽  
Author(s):  
Vimalathithan Devaraj ◽  
Biplab Bose

Epithelial to Mesenchymal Transition (EMT) is a multi-state process. Here, we investigated phenotypic state transition dynamics of Epidermal Growth Factor (EGF)-induced EMT in a breast cancer cell line MDA-MB-468. We have defined phenotypic states of these cells in terms of their morphologies and have shown that these cells have three distinct morphological states—cobble, spindle, and circular. The spindle and circular states are the migratory phenotypes. Using quantitative image analysis and mathematical modeling, we have deciphered state transition trajectories in different experimental conditions. This analysis shows that the phenotypic state transition during EGF-induced EMT in these cells is reversible, and depends upon the dose of EGF and level of phosphorylation of the EGF receptor (EGFR). The dominant reversible state transition trajectory in this system was cobble to circular to spindle to cobble. We have observed that there exists an ultrasensitive on/off switch involving phospho-EGFR that decides the transition of cells in and out of the circular state. In general, our observations can be explained by the conventional quasi-potential landscape model for phenotypic state transition. As an alternative to this model, we have proposed a simpler discretized energy-level model to explain the observed state transition dynamics.


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