Mathematical Modeling of Plasticity and Heterogeneity in EMT.

The epithelial-mesenchymal transition (EMT) and the corresponding reverse process, mesenchymal-epithelial transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at both biochemical and morphological levels. A recent surge in identifying the molecular mechanisms underlying EMT/MET has led to the development of various mathematical models that have contributed to our improved understanding of dynamics at single-cell and population levels: (a) multi-stability-how many phenotypes can cells attain during an EMT/MET?, (b) reversibility/irreversibility-what time and/or concentration of an EMT inducer marks the "tipping point" when cells induced to undergo EMT cannot revert?, (c) symmetry in EMT/MET-do cells take the same path when reverting as they took during the induction of EMT?, and (d) non-cell autonomous mechanisms-how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT? These dynamical traits may facilitate a heterogenous response within a cell population undergoing EMT/MET. Here, we present a few examples of designing different mathematical models that can contribute to decoding EMT/MET dynamics.