Extending Boolean Models to Capture Hybrid Epithelial–Mesenchymal Phenotypes

Epithelial-mesenchymal plasticity (EMP) is a key axis of phenotypic plasticity underlying cancer metastasis. Although hybrid epithelial–mesenchymal (E/M) phenotypes are rare, they drive metastasis through collective migration, stemness, and drug resistance. Classical Boolean models of EMP gene regulatory networks (GRNs) explain the abundance and stability of pure epithelial and mesenchymal states but fail to capture the partial gene-expression profiles that define hybrid phenotypes.

We developed a multilevel extension of Boolean models that incorporates intermediate gene-expression states, enabling a more faithful representation of hybrid phenotypes. This approach identifies hybrid states with partial expression of epithelial and mesenchymal genes that exhibit reduced frustration—indicating fewer conflicting regulatory constraints—and greater stability than their Boolean counterparts. Unlike conventional Boolean hybrids, which depend on update rules or other modeling assumptions, multilevel hybrids emerge robustly across conditions. Stochastic perturbation analyses further reveal that these hybrid states form a dynamic “hybrid cloud,” characterized by frequent transitions among hybrids that preserve metastatic potential while allowing adaptive flexibility. Together, our multilevel framework provides a biologically grounded and mechanistically insightful description of EMP heterogeneity, offering new avenues to understand and predict metastatic progression.