A multilevel formalism to model the hybrid E/M phenotypes in Epithelial-Mesenchymal Plasticity

Epithelial–mesenchymal plasticity (EMP) 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 (GRNs) underlying EMP 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 to their counterparts in classical Boolean models. Furthermore, by resolving dynamical degeneracy, we demonstrate that the hybrid states identified by the multilevel model are more stable. These findings suggest that introducing minimal additional complexity into Boolean models can uncover previously hidden qualitative features of phenotypic landscapes governed by GRNs. Significance Statement Hybrid epithelial-mesenchymal phenotypes drive metastasis through collective migration, stemness, and drug resistance. However, traditional Boolean models of epithelial-mesenchymal plasticity (EMP) networks cannot capture the partial gene expression characteristic of these biologically crucial hybrid states. We developed a multilevel Boolean formalism that extends classical binary models to include intermediate expression levels. This approach successfully captures hybrid states with partial expression of both epithelial and mesenchymal genes, exhibiting lower frustration and greater stability than traditional Boolean hybrid phenotypes. While conventional Boolean hybrid states depend on modeling artifacts, multilevel hybrid states emerge independently of such uncertainties. Critically, plasticity experiments revealed that multilevel hybrid states show significantly higher transition probabilities to other hybrid states compared to traditional models, creating a stable “hybrid cloud” that maintains metastatic properties while allowing adaptive responses to environmental stress. This multilevel framework provides a biologically meaningful characterization of hybrid phenotypes essential for understanding metastasis.