Phase transitions in tumor growth. VI: Epithelial-mesenchymal transition. (English) Zbl 1514.92042
Summary: Herewith we discuss a network model of the epithelial-mesenchymal transition (EMT) based on our previous proposed framework. The EMT appears as a “first order” phase transition process, analogous to the transitions observed in the chemical-physical field. Chiefly, EMT should be considered a transition characterized by a supercritical Andronov-Hopf bifurcation, with the emergence of limit cycle and, consequently, a cascade of saddle-foci Shilnikov’s bifurcations. We eventually show that the entropy production rate is an EMT-dependent function and, as such, its formalism reminds the van der Waals equation.
For Part V, see [R. R. Martin et al., ibid. 486, 762–771 (2017; Zbl 1499.92040)].
For Part V, see [R. R. Martin et al., ibid. 486, 762–771 (2017; Zbl 1499.92040)].
MSC:
| 92C50 | Medical applications (general) |
| 92C37 | Cell biology |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
Keywords:
biological phase transition; entropy production rate; epithelial-mesenchymal transition; tumor-microenvironment cross-talk; phenotypic transitions in cancer cell evolutionCitations:
Zbl 1499.92040References:
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