A multilevel formalism to model the hybrid E/M phenotypes in epithelial-mesenchymal plasticity

Epithelial-mesenchymal plasticity is a cell-fate switching program that enables cells to adopt a spectrum of phenotypes ranging from epithelial (E) to mesenchymal (M), including intermediate hybrid E/M states. Hybrid E/M phenotypes are conducive to cancer metastasis, as they are associated with metastatic initiation, cancer stemness, drug resistance, and collective migration. Boolean models of the gene regulatory networks underlying epithelial-mesenchymal plasticity have yielded valuable insights into the dynamics of E and M phenotypes. However, these models are limited in their ability to capture hybrid phenotypes effectively, as they restrict gene expression to binary states. In contrast, hybrid E/M cells often exhibit partial expression of epithelial and mesenchymal markers. To overcome this limitation, we modified a threshold-based Boolean formalism to incorporate intermediate gene expression levels. The resulting multilevel model reveals novel hybrid steady states characterized by partial expression of both E and M genes, thereby expanding the phenotypic landscape beyond that represented by traditional Boolean approaches. Notably, these hybrid states exhibit lower frustration compared with their counterparts in classical Boolean models. By resolving dynamical degeneracy, we demonstrate that the hybrid states identified by the multilevel model are more stable. Furthermore, the multilevel hybrid states are found to be highly heterogeneous and more plastic than the Boolean hybrid states, with enhanced hybrid-to-hybrid plasticity that can better explain sustained collective migration during metastasis. These findings suggest that introducing minimal additional complexity into Boolean models can uncover previously hidden qualitative features of phenotypic landscapes governed by gene regulatory networks.