  Epithelial to mesenchymal transition (EMT) plays important roles in embryonic
development, tissue regeneration and cancer metastasis. While several feedback
loops have been shown to regulate EMT, it remains elusive how they coordinately
modulate EMT response to TGF-\beta treatment. We construct a mathematical model
for the core regulatory network controlling TGF-\beta-induced EMT. Through
deterministic analyses and stochastic simulations, we show that EMT is a
sequential two-step program that an epithelial cell first transits to partial
EMT then to the mesenchymal state, depending on the strength and duration of
TGF-\beta stimulation. Mechanistically the system is governed by coupled
reversible and irreversible bistable switches. The SNAIL1/miR-34 double
negative feedback loop is responsible for the reversible switch and regulates
the initiation of EMT, while the ZEB/miR-200 feedback loop is accountable for
the irreversible switch and controls the establishment of the mesenchymal
state. Furthermore, an autocrine TGF-\beta/miR-200 feedback loop makes the
second switch irreversible, modulating the maintenance of EMT. Such coupled
bistable switches are robust to parameter variation and molecular noise. We
provide a mechanistic explanation on multiple experimental observations. The
model makes several explicit predictions on hysteretic dynamic behaviors,
system response to pulsed stimulation and various perturbations, which can be
straightforwardly tested.
